Michael Gove is facing threats of legal action after naming Muslim organisations that could fall foul of a new definition of extremism.

Amid free speech fears among Conservatives, the communities secretary told MPs that the advocacy groups Muslim Association of Britain (MAB), Mend and Cage were organisations with “Islamist orientation and beliefs” that could be included on a list of groups banned from access to public money, ministers and civil servants.

In response, the MAB and Mend have challenged Gove to repeat the allegations without parliamentary privilege so they can sue.

The Muslim Council of Britain (MCB), the UK’s biggest Muslim organisation, has consulted lawyers in anticipation of seeking a judicial review if banned from Whitehall and Westminster.

Gove also named the British National Socialist Movement and Patriotic Alternative as groups that promoted neo-Nazi ideology that would also be examined.

Gove told MPs: “Organisations such as the Muslim Association of Britain, which is the British affiliate of the Muslim Brotherhood, and other groups such as Cage and Mend give rise to concern for their Islamist orientation and beliefs. We will be holding these and other organisations to account to assess if they meet our definition of extremism, and will take action as appropriate.

“I am sure that we would agree that organisations such as the British National Socialist Movement and Patriotic Alternative, who promote neo-Nazi ideology, argue for forced repatriation, a white ethnostate and the targeting of minority groups for intimidation, are precisely the type of groups about which we should be concerned and whose activities we will assess against the new definition.”

In response, the MAB chair, Raghad Altikriti, said: “If Gove is confident in his views about the Muslim Association of Britain and other organisations, alleging extremist views and a threat to UK society, we challenge him to state them outside parliament.”

Zara Mohammed, the secretary general at the MCB, said she had consulted lawyers over a possible challenge if her group was named, and was “open to considering a group challenge” with others.

Gove was unveiling the government’s new definition of extremism on Thursday. One minister told the Guardian that deep concern about Gove’s plans extended across the government and the Tory backbenches.

“You can’t define extremism in a bubble,” they said. “You need to have the collaboration, and the legal advice to do so, and yet he has got people that deal with extremism, antisemitism, and everyone else in between asking how are you going to conduct this work.

“Why is a list needed? How is it going to be transparent and fair? If we have been in power for more than a decade, surely it would be possible to work through the levers of government in order to deal with concerns about any groups. Giving a minister the ability to blacklist an organisation isn’t reasonable or conservative.”

The former Home Office minister Robert Jenrick told the Commons: “I fear that the definition, though well-intentioned, lands in no man’s land: not going far enough to tackle the real extremists, not doing enough to protect the non-extremists, those people who are simply expressing contrarian views who might find this definition used against them, not perhaps now, but possibly in the future.”

The new definition, which will be distributed across government and Whitehall, will say: “Extremism is the promotion or advancement of an ideology based on violence, hatred or intolerance, that aims to: 1) negate or destroy the fundamental rights and freedoms of others; or 2) undermine, overturn or replace the UK’s system of liberal parliamentary democracy and democratic rights; or 3) intentionally create a permissive environment for others to achieve the results in 1) or 2).”

The previous guidelines, published in 2011, said individuals or groups were defined as extremist if they showed “vocal or active opposition to British fundamental values, including democracy, the rule of law, individual liberty and the mutual respect and tolerance of different faiths and beliefs”.

Waleed Sheikh, a partner at the law firm Leigh Day who specialises in judicial reviews, said the definition was open to a challenge because it was “extremely broad”.

“This definition will undoubtedly have a chilling effect on free speech. Such a broad definition, plainly open to abuse and without an accompanying independent appeals process, would appear ripe for judicial review,” he said.

Government sources said groups that would in effect be cancelled by ministers for falling foul of the new definition would be named in the coming weeks.

There will be no appeals process if a group is labelled as extremist, it is understood, and groups will instead be expected to challenge a ministerial decision in the courts.

The moves follow a sixfold increase in antisemitic incidents and a fourfold jump in anti-Muslim hatred in the UK since Hamas’s terrorist attack on Israel on 7 October.