Boris Johnson is facing calls to launch an independent inquiry into Islamophobia in the Tory party after the former minister Nusrat Ghani claimed she was told her “Muslimness” was “making colleagues uncomfortable”.

The prime minister was dragged into the controversy this weekend as he awaits the findings of a make-or-break investigation into alleged lockdown-busting parties in Downing Street.

No 10 conceded on Sunday that Ghani had raised her concerns personally with Johnson at a meeting in 2020, and said he had responded by encouraging her to make a formal complaint with the Conservative party.

A No 10 spokesperson said: “The Conservative party does not tolerate prejudice or discrimination of any kind.”

Ghani said she had made clear at the time that she did not think the party complaints process was the right way to tackle her allegations.

“He [Johnson] wrote to me that he could not get involved, and suggested I use the internal Conservative party complaint process. This, as I had already pointed out, was very clearly not appropriate for something that happened on government business,” she said. “All I have ever wanted was for his government to take this seriously, investigate properly and ensure no other colleague has to endure this.”

Ghani says that when she was sacked as a junior transport minister in a reshuffle in 2020, Tory whips told her that her “Muslim woman minister status was making colleagues feel uncomfortable”.

She told the Sunday Times: “It was like being punched in the stomach. I felt humiliated and powerless.” She received public support from the cabinet ministers Nadhim Zahawi and Sajid Javid.

Zahawi, the education secretary, called Ghani “a friend, a colleague and a brilliant parliamentarian”, adding: “This has to be investigated properly and racism [rooted] out.”

The deputy prime minister, Dominic Raab, on Sunday urged Ghani to make a formal complaint to the Conservative party, which she had decided not to do and has now made clear she does not think is appropriate.

Calling the allegations “incredibly serious”, Raab declined to say whether he believed his former government colleague, saying he was “not going to get into impugning anyone’s integrity”.

Raab said there would be no investigation by the party unless she submitted a formal complaint.

The Conservative chief whip, Mark Spencer, has identified himself as the person accused of making the remarks. “These accusations are completely false and I consider them to be defamatory. I have never used those words attributed to me,” he tweeted.

An independent inquiry into the Conservative party’s handling of complaints of discrimination said in May last year that there was “clear evidence of a party complaints system in need of overhaul”.

Chaired by Prof Swaran Singh, the review pointed to a “lack of transparency in the complaints process, with no clear decision-making process as to how complaints should progress, and no specified timeframes for resolution.”

As the row deepened on Sunday, the Muslim Council of Britain (MCB) said it was now time for the Equality and Human Rights Commission (EHRC) to carry out a full inquiry into the party to determine if any breaches of the law had taken place.

Zara Mohammed, the secretary general of the MCB, said: “Nusrat Ghani’s testimony of Islamophobia in the Conservative party is shocking but not surprising. That she is experiencing this as a Muslim woman at the top of the party only reinforces the deep-rooted nature of the problem. Institutional Islamophobia in the Conservative party has gone on with impunity for far too long.”

Shockat Patel, a board member of Muslim Engagement and Development (Mend), described Ghani’s allegation as “totally unacceptable” and said her story had “touched a raw nerve” in the Muslim community, particularly among women.

He called for the Conservatives to accept the definition of Islamophobia drawn up by the all-party parliamentary group on British Muslims, which Labour formally adopted in 2019.

“Firstly, we need the Tory party to get their act together and adopt this definition of Islamophobia. Secondly, we need an independent review to specifically address the issue of Islamophobia. The third point is they need education within the Tory party on what constitutes Islamophobia. And this should be delivered by grassroots organisations, which in the past, they have not engaged with,” Patel said.

Johnson’s team is anxiously awaiting a report by the senior civil servant Sue Gray on parties held in Downing Street while Covid restrictions were in place.

Johnson has admitted attending one event on 20 May 2020 to which his principal private secretary had urged colleagues to “bring your own booze”. The prime minister has insisted he believed it was a work event.

Many Tory backbenchers who have not yet called for a vote of no confidence in the prime minister are awaiting the report before deciding whether they believe Johnson’s position is tenable.

The Conservative backbencher Michael Fabricant caused fresh controversy on Sunday by saying it was unlikely Ghani was discriminated against for her faith because “she’s hardly someone who’s obviously a Muslim”.

In the latest of a series of media appearances apparently aimed at shoring up Johnson’s position, Fabricant told LBC: “I think the whole thing actually stinks, the accusation being made by Nus Ghani.

“She’s hardly someone who’s obviously a Muslim. I mean, I had no idea what religion she is. The Labour MP Keith Vaz, who was of south Asian origin, I do know because we discussed it, he’s a Goan Christian; others are Hindus, others are Muslims or whatever. But with her it wasn’t apparent. So it does seem rather a lame excuse to me that she claims she was sacked because of that.”

The Labour chair, Anneliese Dodds, accused the Tories of “doubling down” instead of trying to tackle the problems Ghani had raised.

“It is shameful that instead of treating allegations of Islamophobia with the seriousness they deserve, the Conservatives have spent the day doubling down and refusing to take action,” she said. “Boris Johnson and the Conservatives’ response has been plain offensive. There needs to be an immediate, independent investigation into these serious allegations.”

Dr Halima Begum, chief executive of race equality thinktank the Runnymede Trust, said: “This is an incredibly serious situation. At a bare minimum, the allegation that a minister of the crown was fired for her so-called ‘Muslimness’ would represent a flagrant challenge to our equalities and labour laws.

“The facts and questions about the legality of what has happened here must be urgently investigated by the very highest authority. This cannot simply be left for another civil service enquiry. If the allegations are proven to be true, Nusrat would have been subjected to grossly discriminatory behaviour.

“[Nusrat’s] distress will be felt by every one of the 3 million Muslims in the country, as well as every member of our religious minority communities. All of the political parties need to do more to demonstrate zero tolerance for discrimination, and to prove that religious minorities in this country are respected regardless of their faith.”

The behaviour of Tory whips had already been under intense scrutiny in recent days. The Conservative MP William Wragg has claimed several colleagues were threatened with having investment in their constituencies withdrawn if they voted in defiance of the government. Wragg is expected to discuss those allegations with the Metropolitan police this week.