Muslim groups which prove they are trying to outlaw extremism within their ranks are to receive financial support, Communities Secretary Ruth Kelly says.
Cash will be available for projects that involve women, that build bridges between communities and are in touch with young people, she said.
She said it was "not good enough" to pay lip service to tackling extremism.
But some Muslim groups condemned her, saying the government was trying to create its own "state-sponsored Islam".
In a direct appeal to Muslims, Ms Kelly stressed that tackling the problem of extremism was not theirs alone.
"This is a shared problem ... But I do say that without you fully on side we will fail. Your voice is more powerful than mine and your actions can be more effective.
"Unless moderates can establish themselves at the centre of their communities and faith, extremists could grow in strength and influence."
She added: "In the future, I'm clear that our strategy of funding and engagement must shift significantly towards those organisations that are taking a proactive leadership role in tackling extremists and defending our values."
Holocaust Memorial boycott
"I know this message will be challenging for some. I make no apologies for that. The scale of the threat means doing any less would be a dereliction of our duty."
Ms Kelly was also critical of groups who chose to boycott commemorations, such as Holocaust Memorial Day, although she insisted it was their right to do so.
The Muslim Council of Britain, which has received government grants, has not been involved in the event commemorating the murder of six million Jews by the Nazis, saying it should be expanded to cover all genocides.
But the MCB's deputy secretary general, Dr Daud Abdullah, said Ms Kelly should speak "with the Muslims and not to the Muslims".
''They are proscriptions, ultimatums, meted out to Muslims," he said.
"'If you don't do this - we don't give you this'...these proscriptive methods, I think is not helping."
Islamic Human Rights Commission Chairman Massoud Shadjareh also said he was "deeply concerned" about the speech.
He said: "The deliberate confusion surrounding the word extremism is a ploy by the government to use its financial muscle to socially engineer a new brand of Islam which will be subservient to its foreign policy."
But other Muslim representatives supported Ms Kelly. Dr Khalid Hameed, the High Sheriff of Greater London, said: "The time has come to isolate (extremists) in our society, I think it is a small minority.
"I am happy to note that the government is taking serious note of what is required in terms of supporting the Muslim community."
There have been continuing discussions about multi-culturalism in Britain, following the 7 July attacks on London by British-born suicide bombers.
Ms Kelly spoke out in the wake of Commons leader Jack Straw's call for Muslim women to consider the impact on community relations of wearing full face veils - which has been criticised by some Muslim groups.
Ms Kelly said ultimately the issue was one of "informed personal choice" and no-one was suggesting in a free and democratic country that the state should decide what someone can or cannot wear.
She said many Muslims had privately told her that "Britain is a great place to be a Muslim".
But, she argued, a great deal more needed to be done to "tackle discrimination, whether conscious or unconscious".