The government is to review whether "core British values" should become a compulsory part of the curriculum for 11 to 16-year-olds in England.
Some Muslims say they feel alienated in the UK
In response to last year's London bombings, ministers want to adapt the current citizenship classes in an attempt to make society more unified.
Education minister Bill Rammell criticised "narrow and unhelpful" interpretations of Islam.
He ordered an urgent review of university Islamic courses.
But critics say a government definition of British values would be too vague and that education cannot prevent extremism.
The six-month-long schools review will ask how all children can develop a strong sense of British identity by learning about Britain's culture and traditions, including the contributions from different communities.
Mr Rammell said: "We know that young people of all faiths and of none are more prone to become radicalised than other groups in society.
"This is true in terms of extreme left and extreme right politics, as well as extremist religious views."
Mr Rammell added: "I want to be very clear that none of this is about silencing voices - far from it.
"It is quite legitimate to voice concern, dissent, frustration, even anger. Of course, that must be at the heart of our democracy."
He said: "There is reason to think that in some cases students are being exposed more than any of us would like to wrong-headed influences, under the name of religion.
"In particular, exposed to teachings that either explicitly condone terrorism, or foster a climate of opinion which is at least sympathetic to terrorists' motivation.
"I am worried about this, so are colleagues in government, so above all are Muslims that I have spoken to."
The UK was multicultural but there needed to be a debate about the things shared by all communities, which bound society together, he added.
In a speech at South Bank University, Mr Rammell said the Islam review followed nine months of conversations with Muslim students about their grievances in education.
Mr Rammell said the reviews were in response to the bombings
But Shadow Higher Education Minister Boris Johnson said: "It is not a question of teaching British values; it is a question of teaching British history.
"There is nothing exclusive or divisive in pointing out the fantastic achievements of the British people.
"For 30 years the British education establishment has cow-towed to the doctrines of multiculturalism and they have deprecated all the institutions and symbols that unite the country."
However, Harris Bokhari, from the Muslim Association of Britain, told the BBC's Five Live it was a "knee-jerk reaction" because teaching British values in schools would not have prevented the London bombings.
"What was the reason why these people actually committed these disgusting acts?
"And unfortunately it was our foreign policy, it was the issue of the illegal war, the illegal occupation of Iraq, the war in Afghanistan, the continuing abuses of the Palestinian people, the illegal occupation of Palestine by the Israeli state."
The university review will ask whether religiously oriented courses rely on narrowly interpreted beliefs which might fuel extremism.
It will also look into the spiritual advice available to students and suggest material that might help explain Islam and what it means to be a Muslim in a multi-faith society.
In a separate development, a government-backed study has suggested many Muslims in England face bleak employment prospects and endure poor standards of housing, which fuel feelings of alienation.