Independent Muslim schools must make greater efforts to show pupils a British "common heritage", says the education watchdog for England.
Ofsted says schools need to look out to other communities
Ofsted chief David Bell said schools needed to protect the "cohesion" of an inclusive, multicultural society.
Muslim, Jewish and Evangelical Christian schools must be "intolerant of intolerance".
But his comments were rejected as a "misconception" by the Association of Muslim Schools.
The association's chairman, Dr Mohamed Mukadam, challenged Mr Bell to produce "evidence that Muslim schools are not preparing young people for life in British society".
"I think it's a misconception of Islamic schools and a further example of Islamophobia. For a person in his position to make such a generalised comment beggars belief," said Dr Mukadam.
Mr Bell's speech called for a much greater effort in all types of schools to teach citizenship - with an accompanying survey showing that young people knew little about politics and had no enthusiasm to find out more.
Badly-taught citizenship lessons have previously been criticised by Mr Bell, and in a speech to the Hansard Society, he warned that it was failing to pass on an understanding of democracy, public service and shared values.
He highlighted his particular concern for citizenship in the growing number of independent faith schools - which he said included about 100 Muslim, 100 Evangelical Christian and 50 Jewish schools.
Mr Bell expressed concern about schools which did not teach children enough about a "common heritage" and needed to do more to promote principles of mutual tolerance and social inclusion.
"I worry that many young people are being educated in faith-based schools, with little appreciation of their wider responsibilities and obligations to British society," said Mr Bell.
The Ofsted chief said his forthcoming annual report would make particular reference to Muslim schools.
"Many must adapt their curriculum to ensure that it provides pupils with a broad general knowledge of public institutions and services in England and helps them to acquire an appreciation of and respect for other cultures in a way that promotes tolerance and harmony."
Mr Bell said such questions of religion and cultural identity were "tricky issues". But he argued that "we must not allow our recognition of diversity to become apathy in the face of any challenge to our coherence as a nation".
"I would go further and say that an awareness of our common heritage as British citizens, equal under the law, should enable us to assert with confidence that we are intolerant of intolerance, illiberalism and attitudes and values that demean the place of certain sections of our community, be they women or people living in non-traditional relationships," said Mr Bell.
The Muslim Council of Britain's secretary-general, Iqbal Sacranie, said that with only "3% of Muslim children attending Muslim faith schools, it is astonishing that they have been singled out in this way".
"We consider it highly irresponsible to suggest that the growth of Muslim faith schools poses a threat to 'our coherence as a nation'."
"The issue around schools not adequately fulfilling their responsibility in preparing children for 'their wider responsibility and obligations' is a generic issue affecting all poorly resourced schools," he said.