Prime Minister Tony Blair yesterday challenged moderate Muslim leaders to speak out more against extremists within their communities.
He insisted there must be a "fundamental" debate where potential terrorists' ideology and their sense of grievance against the West must be tackled just as much as their methods.
And he said there was an impression that Muslim leaders sympathised with extremists' grievances but disagreed with their actions.
The premier spoke out in the run-up to the anniversary of the July 7 London bombings, in an evidence session before the Commons Liaison Committee, made up of chairs of other MPs' select committees.
His comments also followed a complaint from Muslim Labour MP Sadiq Khan on Monday night that those involved with Government-sponsored Muslim working groups were now disillusioned with ministers.
Mr Blair's comments provoked a backlash, with Mohammed Shafiq, of the Ramadhan Foundation, a Manchester group that works with young people to tackle extremism, accusing him of failing to engage with ordinary young Muslims.
The Tories also weighed in, saying the premier was wrong to say the problem could only be resolved within the Muslim community.
The Prime Minister told the MPs: "The Government has its role to play in this, but, honestly, the Government itself is not going to defeat this.
"If we want to defeat the extremism, we have got to defeat its ideas and we have got to address the completely false sense of grievance against the West.
"I am not the person to go into the Muslim community and explain to them that this extreme view is not the true face of Islam."
Shadow home secretary David Davies said: "Sadiq Khan is right to be disappointed by the lack of progress in the Government's response to 7/7.
"It is vital that we keep up the pressure to ensure that every action is taken to achieve integration, respect and understanding of and by all communities in our country."
And shadow attorney general Dominic Grieve added: "If we are to succeed in promoting better integration, and with it a reduction in Islamaphobia, this requires a major effort. The Prime Minister gives the impression this is a problem to be resolved in the Muslim community. I disagree - this is a collective problem."
Inayat Bunglawala, spokesman for the Muslim Council of Britain, accepted that British Muslims have a "crucial" role to play in combating extremist ideas. But he said the Government should also accept its own responsibility for giving extremists "causes to exploit".