The death of Osama bin Laden was a "strike at the heart" of international terrorism, David Cameron told MPs.
He hoped the news would bring a "sense of justice being served" to families of the victims of the atrocities carried out by al-Qa'ida.
But in a Commons statement the Prime Minister warned: "While bin Laden is gone, the threat of al-Qa'ida remains."
Al-Qa'ida and affiliates in Yemen and the Maghreb could launch an operation to demonstrate their continued ability to operate.
Or a "lone wolf" radical could launch a solo attack, he warned.
"We must be more vigilant than ever, and we must maintain that vigilance for some time to come."
The Prime Minister said the al-Qa'ida leader's ability to live in a large house in Pakistan showed he had an "extensive support network" in the country and it was right to ask "searching questions" about that.
He said the UK would continue to co-operate with Pakistan and honour its aid promises because it was in "Britain's national interest" to recognise the two countries' shared struggle against terrorism.
Mr Cameron said the wave of pro-democracy movements and protests sweeping the Arab world showed people were rejecting bin Laden and al-Qa'ida's "poisonous ideology".
Mr Cameron was informed about the US special forces raid on bin Laden's compound in Abbottabad in a phone call from Barack Obama at 3am yesterday.
To murmurs of approval, he said: "I am sure the whole House will join me in congratulating President Obama and praising the courage and skill of the American special forces who carried out this operation."
He continued: "It is a strike at the heart of international terrorism and a great achievement for America and for all who have joined in the long struggle to defeat al-Qa'ida."
Listing the atrocities carried out or inspired by bin Laden, including the 9/11 attacks and the July 7 bombings in London, Mr Cameron said the terrorist was "a man who posed as a leader of Muslims but was actually a mass murderer of Muslims all over the world".
He added: "I hope that, at least for the victims' families, there is now some sense of justice being served as a long, dark chapter in their lives is finally closed."
Turning to the security implications of bin Laden's death, Mr Cameron said: "While bin Laden is gone, the threat of al-Qa'ida remains.
"Clearly, there is a risk that al-Qa'ida and its affiliates in places like Yemen and the Maghreb will want to demonstrate that they are able to operate effectively.
"And of course there is always the risk of a radicalised individual acting alone, a so-called lone wolf attack.
"So we must be more vigilant than ever and we must maintain that vigilance for some time to come."
The terror threat level was already "severe" and updated advice had been given to Britons travelling overseas.
Embassies had also been ordered to review their security arrangements.
Mr Cameron, who has been critical of Pakistan's efforts to combat terrorism in the past, said it was important to work with democrats in the country.
He said: "The fact that bin Laden was living in a large house in a populated area suggests that he must have had an extensive support network in Pakistan."
He added that "we don't currently know the extent of that network, so it is right that we ask searching questions about it".
Mr Cameron told MPs that "Pakistan has suffered more from terrorism than any other country in the world" and "Osama bin Laden was an enemy of Pakistan".
"He had declared war against the Pakistani people. And he had ordered attacks against them.
"President Obama said in his statement 'Counter-terrorism cooperation with Pakistan helped lead us to bin Laden and the compound where he was hiding'.
"Continued co-operation will be just as important in the days ahead.
"I believe it is in Britain's national interest to recognise that with Pakistan we share the same struggle against terrorism.
"That is why we will continue to work with our Pakistani counterparts on intelligence-gathering, tracing plots and taking action to stop them.
"It's why we will continue to honour our aid promises - including our support for education as a critical way of helping the next generation of Pakistanis to turn their back on extremism.
"But above all, it's why we were one of the founder members of the Friends of Democratic Pakistan, because I believe it is by working with the democrats in Pakistan that we can make sure the whole country shares the same determination to fight terror and terrorism."
The Prime Minister said the demise of bin Laden would provide a fresh opportunity for co-operation between Pakistan and Afghanistan to achieve stability on both sides of the border.
It would also provide the opportunity to send a message to the Taliban to break their links with al-Qa'ida and take part in a "peaceful political process".
Mr Cameron said: "The myth of bin Laden was one of a freedom fighter, living in austerity and risking his life for the cause as he moved around in the hills and mountainous caverns of the tribal areas.
"The reality of bin Laden was very different: a man who encouraged others to make the ultimate sacrifice while he himself hid in the comfort of a large, expensive villa in Pakistan, experiencing none of the hardship he expected his supporters to endure."
Mr Cameron, who also updated MPs on the latest news of the military action in Colonel Muammar Gaddafi's Libya, claimed the Arab world was rejecting al-Qa'ida.
He said: "Bin Laden and Gaddafi were said to have hated each other. But there was a common thread running between them.
"They both feared the idea that democracy and civil rights could take hold in the Arab world."
He added: "For twenty years, bin Laden claimed that the future of the Muslim world would be his.
"But what Libya has shown - as Egypt and Tunisia before it - is that people are rejecting everything that bin Laden stood for.
"Instead of replacing dictatorship with his extremist totalitarianism, they are choosing democracy.
"Ten years on from the terrible tragedy of 9/11, with the end of bin Laden and the democratic awakening across the Arab world, we must seize this unique opportunity to deliver a decisive break with the forces of al-Qa'ida and its poisonous ideology which has caused so much suffering for so many years."
Labour leader Ed Miliband said: "The world is a better and safer place without bin Laden commanding or inciting acts of terror."
He welcomed the "co-operative and calm response of the Pakistani government" but said there was a "great deal of uncertainty" about who was aware of bin Laden's presence in the country "especially given his proximity to Pakistani military bases".
Mr Miliband backed the call for increased vigilance, warning that "al-Qa'ida has suffered a serious blow but it remains a threat".
He said the 9/11 attack was "one of the most horrific events of our generation.
"For the victims and their families, including in this country, nothing can remove the pain they feel.
"But the death of Osama bin Laden sends out a clear message: that in the face of terrorist acts the world will not rest until justice is done."
Labour former foreign secretary Jack Straw spoke of the "pernicious ideology" of al-Qa'ida, which remained "the most enduring threat" posed by the group.
"Although there's no silver bullet as far as here at home is concerned, we do need to continue programmes to deal with under-achievement by some, not all, Asian heritage groups in schools and under-employment by them at work in order to reduce the opportunities for their minds to be taken over by this ideology," he said.
Mr Cameron said under-achievement was a problem but "separate to that is the whole bin Laden, al-Qa'ida, extremist, Islamist thread of painting Muslims and Muslim communities as perpetual victims".
He added: "It's absolutely key that we target that ideology and challenge it because it is only in the end by challenging the ideology that we will win this battle."
Liberal Democrat former leader Sir Menzies Campbell urged caution over bin Laden's death.
"The sober reality is that some things are unchanged by the death of Osama bin Laden," he said.
"The threat remains, jihadism must be confronted, and adequate resources, effective international co-operation and good intelligence remain essential."
The PM said there was indeed still a threat from al-Qa'ida but added: "Clearly the end of bin Laden, who was the leader and inspiration of this movement, is a massive setback for al-Qa'ida and for its terrorist affiliates."
The remaining senior leadership of al-Qa'ida now needed to be found in the tribal lands of Pakistan, Mr Cameron said.
Tory Richard Ottaway, chair of the Foreign Affairs Select Committee, said Pakistan was a "divided and complex country" and the death of bin Laden would only exacerbate tensions there.
"Our priority should be to assist Pakistan in remaining a stable state, if only because one, they are a nuclear power and two, they will have an absolutely crucial role to play in any settlement in Afghanistan," he said.
Mr Cameron replied: "Of course there are frustrations and questions that will be asked about who knew what in Pakistan and how could this man live in such a large house in such a comfortable-looking community so close to military installations.
"But I'm absolutely clear the British interest is working with the democratic politicians of Pakistan to deal with the shared issues we have - combating extremism, making sure we're dealing with a safe rather than a dangerous nuclear power and reaching a settlement in Afghanistan so we can bring Britain's brave troops home."
Labour former Cabinet minister Hazel Blears said: "You will know that the vast majority of Muslims in this country entirely reject the violent ideology of al-Qa'ida and Osama bin Laden.
"Would you therefore confirm that in the review of the Prevent programme going forward, you will ensure that you put in place a series of practical programmes to build the resilience of our young people to these messages of hatred and extremism?"
She urged the PM to "take really seriously" the challenge to al-Qa'ida's ideology.
Mr Cameron replied: "I think the problem has been not that a minority of British Muslims actually back al-Qa'ida, it's not so much that.
"It's that there has been an ideology, pernicious in some communities amongst a minority, that has given some comfort to the stories that al-Qa'ida provide about victimhood and the rest of it.
"You have to address that issue in order to drain the swamp in which al-Qa'ida's been swimming."
Lib Dem Julian Huppert (Cambridge) said it was clearly good that bin Laden's influence had ended but said it was a "great shame we were not able to bring him before a court".
Mr Cameron said: "I listened very carefully to (White House counterterrorism chief) John Brennan's briefing and he made clear that they were prepared to take bin Laden alive and to capture him but only if it wasn't a situation in which they were actually in a firefight and at risk themselves.
"I think the Americans were completely justified in what they did and I think the world is much better off without him."
Tory Julian Lewis (New Forest E) said too many Muslims "do not even accept that bin Laden was responsible for 9/11".
He asked: "What does this say about the failure of the West to get the counter-narrative and the counter-propaganda out worldwide and effectively?"
The PM said this did not mean many Muslims were "actively backing bin Laden, it just means they've bought into a narrative into Israeli plots and all the rest of it".
He added: "We've got to challenge that narrative. We can't have young people growing up in our country somehow believing this nonsense."
Tory Tobias Ellwood (Bournemouth E), whose brother Jonathan was killed in the 2002 Bali bombing, said he had visited the UK memorial today to pay his respects.
"News of bin Laden's death didn't fill me with any sense of victory, for the world is no safer, but it did feel that we're starting a new chapter and the world is a better place," he said.
Pakistan-born Baroness Falkner of Margravine, whose father served in that country's military intelligence, said it would have been "pretty impossible" for bin Laden to have remained undetected.
In Lords exchanges on the statement, she congratulated President Obama and the US special forces for "bringing about a closure to the chapter which started on September 11 2001".
"It was a chapter which shook the Muslim world to its very core as well as affecting of course the United States and other countries," said the Liberal Democrat peer.
Describing Pakistan as an "extremely fragile" state, Lady Falkner said there was more doubt about its capability than its commitment to countering terrorism.
Referring to the role of Pakistan's ISI and defence intelligence, she said: "My father was a member of that community so I well know that it would have been pretty impossible for Mr bin Laden to have lived there for as long as he did undetected."
She called for a "constructive, working relationship" between Pakistan and Afghanistan and a rapprochement between India and Pakistan. "All three countries are essential if regional peace and security is to be secured in that most dangerous region."
Labour's Lord Clinton-Davis used the exchanges to call for extra money for the Metropolitan and other police forces to tackle terrorism in the UK.
Responding to historian and crossbench peer Lord Thomas of Swynnerton, Lords Leader Lord Strathclyde said: "No doubt there will be questions of the legality of the US (action), but that's a question between the Pakistani authorities and the US."
Labour's Lord Anderson of Swansea, a former chairman of the Commons foreign affairs committee, told the minister: "You are right that we should rejoice at this great achievement." But he said the focus had now shifted to Yemen.
Labour former minister Malcolm Wicks said that when the PM had visited Pakistan last month, he had announced that the UK and Pakistan would exchange knowledge on how to counter roadside bombs.
Mr Wicks asked: "Would you, in the light of very recent events, review that co-operative agreement, lest technical knowledge gained could be passed into the hands of terrorists rather quickly in Afghanistan and elsewhere, with consequent threats to British and other lives?"
Mr Cameron replied: "Of course we look at all of these things very carefully but the point I would make is that Pakistan has lost thousands of soldiers fighting extremists in South Waziristan, in the Swat Valley, where they are trying to root out a similar sort of Taliban to what we are fighting in Afghanistan.
"You have to understand, when you speak to President Zadari, this is someone who lost his wife to extremist terrorists.
"So of course we must be careful in all that we do but I think actually working with the Pakistanis so they can combat the extremism in their own country is clearly in our national interest."
Tory Geoffrey Clifton-Brown (The Cotswolds) said it was "imperative" that the Government continue to provide assistance to Pakistan.
The PM said: "We do need to be clear with the Pakistanis about what we hope to gain from the partnership that we enter into, and clearly work on counter-terrorism is absolutely vital for Britain's national interest, but we are prepared to do a huge amount with Pakistan to help with issues like education of children."
He added: "Clearly if we want to keep those people away from extremism and indeed if we want to deal with problems of migration as well, it makes sense for us to continue with our aid programme."
Labour's Mark Hendrick (Preston) asked whether the PM agreed that the swift sea burial of bin Laden would lead to conspiracy theories over whether he was still alive.
Mr Cameron said: "I think frankly that the US took a sensible decision on the basis that this was in line with all the correct Muslim practices for burial, incidentally a luxury that bin Laden never allowed to any of his victims.
"And this was done in an appropriate way at sea and I think they should be commended for doing it in that way."
Tory Jason McCartney (Colne Valley) said it would be "inappropriate" if the US chose to release "gory footage" of the operation in Pakistan.
Mr Cameron said this was a decision for the US to make.
"The only thing I would say, from my limited experience of this, is that there are some conspiracy theorists who will never be satisfied," he said.
"There are some people who still believe that Elvis will be found riding Shergar. You will never satisfy some people. So I think that what the Americans have done so far is pretty sufficient in explaining to all reasonable people that bin Laden is no more."Reuse content