David Cameron has criticised "state multiculturalism" in his first speech as prime minister on radicalisation and the causes of terrorism.
At a security conference in Munich, he argued the UK needed a stronger national identity to prevent people turning to all kinds of extremism.
He also signalled a tougher stance on groups promoting Islamist extremism.
The speech angered some Muslim groups, while others queried its timing amid an English Defence League rally in the UK.
As Mr Cameron outlined his vision, he suggested there would be greater scrutiny of some Muslim groups which get public money but do little to tackle extremism.
Ministers should refuse to share platforms or engage with such groups, which should be denied access to public funds and barred from spreading their message in universities and prisons, he argued.
"Frankly, we need a lot less of the passive tolerance of recent years and much more active, muscular liberalism," the prime minister said.
"Let's properly judge these organisations: Do they believe in universal human rights - including for women and people of other faiths? Do they believe in equality of all before the law? Do they believe in democracy and the right of people to elect their own government? Do they encourage integration or separatism?
"These are the sorts of questions we need to ask. Fail these tests and the presumption should be not to engage with organisations," he added.
The Labour MP for Luton South, Gavin Shuker, asked if it was wise for Mr Cameron to make the speech on the same day the English Defence League staged a major protest in his constituency.
There was further criticism from Labour's Sadiq Khan whose comments made in a Daily Mirror article sparked a row.
The shadow justice secretary was reported as saying Mr Cameron was "writing propaganda material for the EDL".
Conservative Party chairman Baroness Warsi hit back, saying that "to smear the prime minister as a right wing extremist is outrageous and irresponsible". She called on Labour leader Ed Miliband to disown the remarks.
Meanwhile, the Muslim Council of Britain's assistant secretary general, Dr Faisal Hanjra, described Mr Cameron's speech as "disappointing".
He told Radio 4's Today programme: "We were hoping that with a new government, with a new coalition that there'd be a change in emphasis in terms of counter-terrorism and dealing with the problem at hand.
"In terms of the approach to tackling terrorism though it doesn't seem to be particularly new.
"Again it just seems the Muslim community is very much in the spotlight, being treated as part of the problem as opposed to part of the solution."
In the speech, Mr Cameron drew a clear distinction between Islam the religion and what he described as "Islamist extremism" - a political ideology he said attracted people who feel "rootless" within their own countries.
"We need to be clear: Islamist extremism and Islam are not the same thing," he said.
The government is currently reviewing its policy to prevent violent extremism, known as Prevent, which is a key part of its wider counter-terrorism strategy.
A genuinely liberal country "believes in certain values and actively promotes them", Mr Cameron said.
"Freedom of speech. Freedom of worship. Democracy. The rule of law. Equal rights, regardless of race, sex or sexuality.
"It says to its citizens: This is what defines us as a society. To belong here is to believe these things."
He said under the "doctrine of state multiculturalism", different cultures have been encouraged to live separate lives.
'I am a Londoner too'
"We have failed to provide a vision of society to which they feel they want to belong. We have even tolerated these segregated communities behaving in ways that run counter to our values."
Building a stronger sense of national and local identity holds "the key to achieving true cohesion" by allowing people to say "I am a Muslim, I am a Hindu, I am a Christian, but I am a Londoner... too", he said.
Security minister Baroness Neville-Jones said when Mr Cameron expressed his opposition to extremism, he meant all forms, not just Islamist extremism.
"There's a widespread feeling in the country that we're less united behind values than we need to be," she told Today.
"There are things the government can do to give a lead and encourage participation in society, including all minorities."
But the Islamic Society of Britain's Ajmal Masroor said the prime minister did not appreciate the nature of the problem.
"I think he's confusing a couple of issues: national identity and multiculturalism along with extremism are not connected. Extremism comes about as a result of several other factors," he told BBC Radio 5 live.
Former home secretary David Blunkett said while it was right the government promoted national identity, it had undermined its own policy by threatening to withdraw citizenship lessons from schools.
He accused Education Secretary Michael Gove of threatening to remove the subject from the national curriculum of secondary schools in England at a time "we've never needed it more".
"It's time the right hand knew what the far-right hand is doing," he said.
"In fact, it's time that the government were able to articulate one policy without immediately undermining it with another."