In his first public speech since becoming director-general in April, Jonathan Evans said the security service was facing "the most immediate and acute peacetime threat" in its 98-year history.
Addressing a Society of Editors Conference in Manchester, he said the number of individuals in Britain identified by MI5 as having links with terrorism had risen from 1,600 last year to at least 2,000.
And he said they suspected there could be a similar number again who they did not know about.
Mr Evans warned they were part of a "deliberate campaign" being waged against Britain by al-Qa'ida - which was extending its tentacles across the Middle East and Africa.
"Terrorist attacks we have seen against the UK are not simply random plots by disparate and fragmented groups," he said.
"The majority of these attacks, successful or otherwise, have taken place because al-Qa'ida has a clear determination to mount terrorist attacks against the United Kingdom.
"This remains the case today, and there is no sign of it reducing."
Mr Evans highlighted the way al-Qa'ida was targeting vulnerable young people as terrorist recruits and warned of the need to protect children from exposure to "violent extremism".
"As I speak, terrorists are methodically and intentionally targeting young people and children in this country," he said.
"They are radicalising, indoctrinating and grooming young, vulnerable people to carry out acts of terrorism. This year, we have seen individuals as young as 15 and 16 implicated in terrorist-related activity."
Mr Evans said the terror plots were being directed from a widening range of countries.
While in the past much of the planning had come from al-Qa'ida's "core leadership" in the tribal areas of Pakistan, there were now signs that al-Qa'ida in Iraq was seeking to promote attacks outside that country while there was terrorist training and planning in Somalia directed against the UK.
Although MI5's main priority was the terrorist threat, Mr Evans said the service was still having to divert resources to counter " unreconstructed attempts" by countries such as Russia and China at Cold War-style espionage.
"It is a matter of some disappointment to me that I still have to devote significant amounts of equipment, money and staff to countering this threat," he said.
"They are resources which I would far rather devote to countering the threat from international terrorism - a threat to the whole international community, not just the UK."
Mr Evans emphasised the need to think "strategically" in countering a terrorist threat that could last for a generation. He said it could not be defeated by the intelligence and security services alone.
"It requires a collective effort in which Government, faith communities and wider civil society have an important part to play," he said.
"And it starts with rejection of the violent extremist ideology across society - although issues of identity, relative deprivation and social integration also form important parts of the backdrop."
While MI5 had expanded since the 9/11 attacks in 2001 - and was expected to reach 4,000 staff by 2011 - he said there was a limit to what intelligence could achieve.
"We cannot know everything. There will be instances when individuals come to the notice of the Security Service or the police but then subsequently carry out acts of terrorism. This is inevitable," he said.
"Every decision to investigate someone entails a decision not to investigate someone else. Knowing of somebody is not the same as knowing all about somebody.
"And it would be perverse for my service to avoid knowing of somebody for fear of being held to blame if they later become involved in an attack.
"I think we should be very careful to bear this in mind when talking about so-called 'intelligence failures'."
Mr Evans said MI5's focus was becoming increasingly regional, with eight offices across Great Britain, and around 25% of the staff expected to be working outside its London headquarters by 2011.
At the same time, a new Northern Ireland headquarters building will be opened shortly, with the capacity to contribute to MI5's overall counter-terrorism effort as well as particular issues relating to the province.
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