A school is not protecting its pupils from the possible risks of extremism and should go into special measures, an Ofsted report has said.
Governors at Carlton Bolling College, Bradford, met the needs of Muslim students, but did not take sufficient account of other faiths, it said.
The report, seen by the BBC, said students needed more opportunities "to recognise extremist views".
Faisal Khan, chair of the governors, said it was "full of inaccuracies".
David Green, leader of Bradford Council, said he had asked the Department for Education to allow the council to send in an interim executive board to replace the governing body.
Mr Green said: "I firmly believe you need to teach all religions to ensure people understand, and are aware of, the multicultural and multi religious society in which we live.
"All schools should teach all religions."
He said the council had "a grip of all schools" it was responsible for and the national curriculum was "being taught properly".
"Not all governors agreed with some of the activities that have been reported", he added.
David Ward, the Liberal Democrat MP for Bradford East and a former governor at the school, said: " Young people have a right to a good education and if the governing body is standing in the way of that it needs to move over and let somebody else take over.
Ed Thomas, North of England correspondent
The BBC has seen a leaked Ofsted report.
It is unpublished but details the inspectors' concerns that students are at possible risk from extremism.
The leader of Bradford council, David Green, denied there was an "Islamic agenda" at schools in the city.
He said the council had been talking to Ofsted for months about a problem within the governing body and will now replace the governors.
The BBC has spoken exclusively to a former governor at the school, who asked to remain anonymous.
She said she left on protest at what was happening there.
She said: "It's not a faith school and if it was to become so, that would have to be for the school to decide not a minority of governors on the governing body".
Outside the school some parents spoke in the college's support.
Saba Azeem, a mother with three children at the school, said it was "a good school, with no Islamic agenda".
The Department for Education said it had received an application from the council to remove the governing body at the school and was considering what to do next.
"What you can't have is young people who go through a school experience without the British values of tolerance, understanding of other faiths and preparation for living in a multicultural, multi-faith world."
The education watchdog report, which has not been published, found the secular state school, its governance and its leadership were "inadequate".
The report continued: "Some governing body members have also pushed for the narrowing of the geography curriculum and restricting Religious Education courses to the study of Islam.
"The college does not protect students from the possible risks posed by extremism well enough.
"Students do not have enough opportunities to understand how to recognise extremist views or what to do if they hear such views expressed."
A high proportion of the 1,500 students at the school are of minority ethnic heritage. The largest groups are of Pakistani and Bangladeshi heritage.
A small proportion of the pupils are classed as "white British" and a small but increasing minority are of eastern European heritage, the report said.
It comes a month after the BBC learnt teachers in Bradford had reported some governors were promoting a more Islamic ethos.
Ofsted said there was "deep-rooted disagreement and distrust" between the school's governors.
The leadership of the school was hindered by the divisions and some staff had told inspectors they feared speaking out, the report said.
The inspectors were told Faisal Khan, chairman of the governing body, shouted aggressively when he heard views contrary to his own.
Mr Khan has told the BBC the Ofsted report was "full of inaccuracies".
He was a former governor at the city's Laisterdyke Business and Enterprise College where a different Ofsted report said governors' actions were "increasingly undermining the capacity of senior leaders".
Bradford Council replaced the board of governors with an interim executive board at the school in May.
The latest report said some Carlton Bolling College governors had also exerted pressure on head teachers to exempt the college from having a broadly Christian act of worship.
Proposals for a mixed residential school trip to London were refused by governors and boys were excluded from the trip.
Overall, the report found "governors do not discharge their responsibilities to ensure equality of opportunity for all pupils".
The previous Ofsted report, in January 2013, found the school should be rated "good" but there had been significant change in leadership and staffing over the past 18 months, including two head teachers and an acting head teacher.
More than 20 teachers have either left the school or are about to leave, the report said.
The inspector's report made a number of recommendations, including an immediate review to make the governing body "fit for purpose".
It also recommends training for both staff and governors on how to "identify, and respond to possible risks to students from extreme or radical views so they can better safeguard students from such risks".
Nearly a quarter of Bradford's population are Muslim, and the city is home to the largest proportion of people of Pakistani ethnic origin - 20.4% - in England, according to the 2011 National Census.
Last month, Ofsted published reports on 21 schools in Birmingham after allegations of a hardline Muslim takeover of schools there.
The inspectors' report said head teachers had been "marginalised or forced out of their jobs", and there was evidence of an "organised campaign to target certain schools".