The Conservative party chair, Baroness Warsi, has been banned by David Cameron from attending a major Islamic conference today, igniting a bitter internal row over how the government tackles Islamist extremism.

Warsi, Britain's first female Muslim cabinet minister, was told by the prime minister to cancel her appearance at the Global Peace and Unity Event, which is being billed as the largest multicultural gathering in Europe.

The London-based conference is aimed at improving community relations, yet critics have pointed out that a number of speakers who are due to appear have justified suicide attacks and promoted al-Qaida, homophobia and terrorism.

An influential voice among the international Muslim community, Warsi believes that confronting extremists at public events is a more effective way to tackle fundamentalism than a refusal to engage with them. A Whitehall source said: "She had hoped to attend, but there is a conflict of opinion on how extremists should be dealt with and the prime minister, supported by Theresa May [the home secretary], were adamant no Tories should attend."

Paul Goodman, the former Tory communities minister, said: "The aim of the organisers is to exploit politicians by using their presence to gain muscle, influence and credibility among British Muslims. Politicians shouldn't play their game."

Argument over the most effective strategy to challenge extremism has also led to a schism between the Liberal Democrats and Conservatives in the coalition government. While Cameron has prohibited Tories from attending the event at the Excel Centre in Docklands, the deputy prime minister, Nick Clegg, has firmly opposed a boycott by politicians, agreeing with Warsi that extremists should be publicly confronted.

A compromise agreement means that Andrew Stunell, the Liberal Democrat communities minister, will today deliver an aggressive speech against those who espouse fundamentalism. "He will make clear that the coalition government will not tolerate extremism, hatred and intolerance in any form," said a spokesman for the Department for Communities and Local Government.

It is also understood that Clegg will send a message to the conference reiterating the need to tackle extremism head-on. Other political speakers include the shadow justice secretary, Sadiq Khan, a campaign adviser to the Labour leader, Ed Miliband.

The conference, which is expected to draw up to 60,000 visitors, is likely to witness clashes between moderate Muslims and extremists. One influential Muslim scholar, Tahir ul-Qadri from Pakistan, will denounce those in the audience who subscribe to terrorism as "disbelievers". Qadri, whose spokesman confirmed that he had hired a large security team after receiving death threats, expects a hostile reception from elements of the crowd. The spokesman added: "We want to bring a moderate view of Islam to a new audience, not just preach to the converted."

The conference has been organised by Britain's most popular Muslim television station, the Islam Channel, which earlier this year was accused by a Muslim thinktank, the Quilliam Foundation, of promoting extremist groups. The Quilliam report added that the channel's chief executive and principal conference organiser, Mohammed Ali Harrath, has a conviction in Tunisia for terrorism-related offences. Harrath insists that his Tunisian organisation is a non-violent political party.

Critics say there are more hardline speakers at the event than in previous years. Controversial figures include a former Pakistani government minister, Muhammad Ijaz-ul-Haq, who has been quoted as saying that the award of a knighthood to the author Salman Rushdie in 2007 justifies suicide attacks.

Another is Sheikh Shady al-Suleiman, from Sydney, who was in charge of youth events at an Australian mosque when it invited Anwar al-Awlaki, a radical al-Qaida preacher linked to two of the 9/11 hijackers and the Detroit plane bomber, to speak. Al-Suleiman has also supported the stoning of adulterers.

Speakers also include Abdur Rashid Turabi, head of Pakistan's extremist Jamaat-e-Islami party, whose former leader, Qazi Hussain Ahmed, said he saluted a suicide bomber for killing five American soldiers and earlier this month had his UK visa revoked by the Home Office. Sheikh Yasir Qadhi, who has said that homosexuality is an "aberration against God", is also due to attend.