Michelle Donelan sparked an outcry when she said universities will face a legal duty requiring them to allow in the likes of historian David Irving – with the threat of fines if they did not.
“Obviously it would depend on what they are saying, whether they were straying into racism or straying into hate crimes,” Ms Donelan said.
The minister was then pushed on whether Holocaust deniers would have the right to speak – and could demand compensation if blocked – because such denial is lawful in this country.
“There is a difference between condoning and supporting something when standing up for free speech,” she replied, on BBC Radio 4.
But, after the comments were widely criticised, Boris Johnson’s spokesman contradicted Ms Donelan, saying: “Holocaust denial is not something that the government would ever accept.”
Asked if the prime minister agreed with the minister, the spokesman replied: “No” – and, asked if he believed Holocaust denial is antisemitic, he said: “Yes.”
Ms Donelan’s comments came despite her recently criticising higher education institutions that have refused to back the international definition of antisemitism.
“I urge all universities to adopt it. If not, then we will have to be forced into taking action to ensure that they do,” she told the Commons education committee.
Gavin Williamson, the education secretary, has now directly threatened them with financial penalties if they continue to challenge the definition..
“If universities ignore the issue, I have asked officials to consider options e.g. directing the Office for Students to impose a new registration condition or suspending funding,” he tweeted.
Ministers have claimed the Higher Education (Freedom of Speech) Bill will encourage “open intellectual debate” and counter the “chilling effect of censorship on campus”.
For the first time, student unions will be legally obliged to protect freedom of speech and could be taken to court by cancelled speakers.
But universities have dismissed the new laws as unnecessary, warning of increased bureaucracy and insisting free-speech problems on campus are being hugely exaggerated.
Ms Donelan later sought to clarify her comments on Twitter, saying: “Some people have asked me how this interacts with the government’s work to combat antisemitism.
“Let me be clear antisemitism is abhorrent and will not be tolerated at our universities. This bill will protect and promote lawful free speech.
“Universities will still need to adhere to the Equality Act, the Prevent Duty and ensure that speakers do not incite violence, harassment or hate crimes.”