David Cameron has vowed to "aggressively" pursue and disrupt extremists trying to spread the "poisonous ideology" of radical Islamism.
Launching the Government's counter-extremism strategy, the Prime Minister warned it was no time for "kid gloves" when faced with the threat to Britain's values of democracy, equality and tolerance.
He challenged Muslim communities to "own" the problem, saying that ultimately it was the "silent majority" who rejected extremism who were key to driving out the radicals.
The strategy document emphasised the need to root out extremism across a wide range of institutions including schools, universities, local councils, the National Health Service, charities and prisons.
While extremism had to be combated in all its forms- including neo-Nazism, Islamophobia and anti-Semitism - Mr Cameron said that it was the fight against Islamist extremism, which represented "one of the great struggles of our generation.
Writing in the foreword, he said: "In responding to this poisonous ideology, we face a choice. Do we close our eyes, put our kid gloves on and just hope that our values will somehow endure in the end? Or do we get out there and make the case for those values, defend them with all that we've got and resolve to win the battle of ideas all over again?
"In the past, I believe governments made the wrong choice. Whether in the face of Islamist or neo-Nazi extremism, we were too tolerant of intolerance, too afraid to cause offence. We seemed to lack the strength and resolve to stand up for what is right, even when the damage being done by extremists was all too clear."
He said that it was essential to disrupt the activities of the extremists, "aggressively pursuing the key radicalisers" responsible for spreading the ideology of violent jihad.
The plan includes a review of the rules of British citizenship - including strengthening the "good character" consideration and whether an applicant has promoted extremist views.
There will be an extension of powers for passports to be withdrawn from young people at risk of travelling abroad to join groups such as Islamic State (IS).
The mechanism has already been used on several under-16s since it was introduced in July, and will now be available for 16- and 17-year-olds.
There will be bans on radical preachers posting material online, and internet firms will work more closely with police to stop extremist material being disseminated.
Anyone with a conviction or civil order for terrorist or extremist activity will also be automatically barred from working with children and vulnerable people.
"The extremist narrative needs to be fought every day at the kitchen table, on the university campus, online and on the airwaves," Mr Cameron said in an article posted on the No 10 website.
"As a government, I know we must own this problem. But our Muslim communities must own it too. We have all got a critical part to play, but I strongly feel the currently silent majority can make all the difference."
However, the Muslim Council of Britain warned that the strategy was "flawed" and counter-productive, and alienated the Muslim communities whose support the Government was seeking.
"Whether it is in mosques, education or charities, the strategy will reinforce perceptions that all aspects of Muslim life must undergo a 'compliance' test to prove our loyalty to this country," said MCB general secretary Shuja Shafi .
"We cannot help but also detect the McCarthyist undertones in the proposal to create blacklists and exclude and ban people deemed to be extremist."