Mr Cameron said that "with hindsight" he would never have recruited the former News of the World editor and said Coulson should face "severe" criminal charges if it turned out that assurances he gave that he knew nothing about phone-hacking were lies.
Fresh questions were also being asked about the Prime Minister's role in the News Corporation bid for BSkyB, after aides admitted that he could not rule out having discussed the deal in private conversations with the company's executives.
Labour said that Mr Cameron's failure to respond to repeated questions in the Commons over whether BSkyB was mentioned in meetings with News International executives including Rebekah Brooks made the Prime Minister look "slippery".
But the PM's office insisted Mr Cameron never had any "inappropriate" conversations about the bid and always ensured he was excluded from the process of reaching a decision on the deal, which was the responsibility of Culture Secretary Jeremy Hunt.
"The Prime Minister couldn't rule out that it was raised with him," said an aide. "But there were no inappropriate conversations had about BSkyB."
MPs were recalled to Parliament for an additional day today to hear an emergency statement from the Prime Minister on the hacking affair and the resignations of Metropolitan Police Commissioner Sir Paul Stephenson and assistant commissioner John Yates.
The statement, and a lengthy debate on the controversy, took place as News Corporation chairman Rupert Murdoch flew back to the US after giving evidence to a parliamentary committee yesterday.
Mr Cameron told the House of Commons he would make a "profound apology" if Mr Coulson's assurances that he knew nothing about phone-hacking during his time as News of the World editor turned out to be wrong.
The PM said he took responsibility for the decision to recruit Mr Coulson as media adviser in 2007 - just months after Mr Coulson resigned from the Sunday tabloid when it emerged that a reporter had hacked phones on his watch - and then to bring him into 10 Downing Street as director of communications after last year's election.
"If it turns out I have been lied to, that would be a moment for a profound apology, and in that event I can tell you I will not fall short," said the Prime Minister.
Mr Cameron acknowledged that if he had known when he appointed Mr Coulson what he knew now, he would never have offered him the job.
"Of course I regret, and I am extremely sorry about the furore it has caused. With 20:20 hindsight and all that has followed I would not have offered him the job and I expect that he wouldn't have taken it," he said.
"But you don't make decisions in hindsight, you make them in the present. You live and you learn and believe you me, I have learned."
Labour leader Ed Miliband accused the Prime Minister of repeatedly ignoring warnings about the danger of keeping Mr Coulson at the heart of government.
These included a report last year in the New York Times in which former News of the World reporter Sean Hoare alleged that hacking was widespread when Coulson was editor.
Mr Miliband said Mr Yates had offered to brief the Prime Minister on the phone-hacking situation last September, but Number 10 chief of staff Ed Llewellyn had rejected the suggestion.
The Labour leader said there appeared to have been "a deliberate attempt to hide from the facts about Mr Coulson".
"The Prime Minister was caught in a tragic conflict of loyalty between the standards of integrity that people should expect of him and his staff and his personal allegiance to Mr Coulson," said Mr Miliband. "He made the wrong choice."
Mr Miliband said that the allegations in the NYT article were taken seriously enough by the Metropolitan Police for the force to end its contract with Mr Coulson's former deputy editor Neil Wallis, but the Prime Minister insisted it included no new information to change his judgment on his communications chief.
The Labour leader suggested Mr Cameron's conflict of interest led to Sir Paul Stephenson's resignation over the weekend after it emerged that the force had hired Mr Wallis as a media adviser.
"Sir Paul Stephenson was trapped," Mr Miliband said. "He was trapped between a Home Secretary angry about not being told about the hiring of Mr Wallis and Sir Paul's belief, in his own words, that doing so would have compromised the Prime Minister."
Mr Miliband added: "It's not about hindsight. It is not about whether Mr Coulson lied to him. It is about all the information that the Prime Minister ignored."
But Mr Cameron accused the Labour leader of "punting feeble conspiracy theories" and said that it would have been "completely wrong" for Mr Llewellyn to accept the offer of a private briefing on police operations.
The PM also dismissed claims that he broke the ministerial code of conduct by meeting News International executives - including Ms Brooks - while Mr Murdoch was bidding to take over BSkyB.
And he said that he was not aware until Sunday that Mr Coulson had recruited Mr Wallis to provide unpaid advice during the Conservative general election campaign last year.
Aides later said that there was no question of Mr Wallis having met the Prime Minister in Downing Street, but said it was possible that he came to Number 10 for meetings with Mr Coulson.
Mr Cameron said that politicians now needed to forego partisan point-scoring and act decisively to deal with the issues raised by the phone-hacking scandal.
He named the full panel who will serve on the judicial inquiry headed by Lord Justice Leveson, including civil liberties campaigner Shami Chakrabarti, former journalists and an ex-police chief. And he extended the inquiry's remit to cover not only the press, but also broadcasters and social media.
Meanwhile, News Corp announced it is to stop paying the legal fees of a private investigator jailed in the phone-hacking scandal.
In a statement, the company said that its management and standards committee had decided to terminate any arrangement to pay the legal fees of Glenn Mulcaire "with immediate effect".
