Downing Street has described remarks made about Diane Abbott by the Conservatives’ biggest donor as “racist and wrong” after senior politicians from across the political spectrum piled pressure on Rishi Sunak to intervene.

No 10 and Conservative ministers initially stopped short of making that criticism of Frank Hester’s remarks, after the Guardian reported on Monday that the businessman said in a 2019 meeting that looking at Abbott made you “want to hate all black women” and said the MP “should be shot”.

However, Sunak’s spokesperson released a new statement on Tuesday evening, after a day in which Kemi Badenoch, the business secretary, Kwasi Kwarteng, the former chancellor, and William Hague, the former Conservative leader, all described Hester’s comments as racist.

Abbott said the remarks were “frightening”, adding that she is a “single woman and that makes me vulnerable anyway, but to hear someone talking like this is worrying”. She said she had made a report about the comments to the Metropolitan police, which is assessing the complaint.

Keir Starmer, the Labour leader, was among those saying the remarks were “abhorrent” and that the Conservatives should hand back the £10m in donations given to the party by Hester and his company.

In its statement, Downing Street said that comments “allegedly made by Frank Hester were racist and wrong”. A spokesperson added that his remorse should be accepted after he “rightly apologised” for the offence caused.

“The prime minister is clear there is no place for racism in public life and as the first British-Asian prime minister leading one of the most ethnically diverse cabinets in our history, the UK is living proof of that fact,” the spokesperson said.

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Earlier, No 10 had stopped short of such a description, and stuck to the line that the remarks were “clearly unacceptable”.

Hester, who has given £10m to the Conservatives, said in the 2019 meeting reported on Monday that he did not hate all black women. But he said that seeing Abbott, who is Britain’s longest-serving black MP, on TV meant “you just want to hate all black women because she’s there”.

After the publication of the remarks, a statement from the healthcare technology firm the Phoenix Partnership (TPP), which Hester runs, said he “accepts that he was rude about Diane Abbott in a private meeting several years ago but his criticism had nothing to do with her gender nor colour of skin”. The statement said Hester “abhorred” racism, “not least because he experienced it as the child of Irish immigrants in the 1970s”.

The statement added: “He rang Diane Abbott twice today to try to apologise directly for the hurt he has caused her, and is deeply sorry for his remarks. He wishes to make it clear that he regards racism as a poison, which has no place in public life.”

TPP’s lawyers have previously said the comments were not a true or accurate characterisation of the company or Hester.

Downing Street’s statement came after Badenoch, who is also the equalities minister, was the most senior Conservative to say the comments were racist, and to criticise them as “appalling”.

In a statement on X on Tuesday, Badenoch said: “Hester’s 2019 comments, as reported, were racist. I welcome his apology. Abbott and I disagree on a lot. But the idea of linking criticism of her, to being a black woman is appalling. It’s never acceptable to conflate someone’s views with the colour of their skin.

“MPs have a difficult job balancing multiple interests – often under threats of intimidation as we saw recently in parliament. Some people make flippant comments without thinking of this context. This is why there needs to be space for forgiveness where there is contrition.”

On Tuesday morning, the energy minister Graham Stuart said while the remarks were “ridiculous” he would “hesitate” to describe them as racist. Other ministers also defended Hester after his apology, saying it was time to “move on”.

Many Conservative MPs remained silent on Tuesday, refusing to comment on Hester’s remarks or whether the Conservative party should return his £10m donations, despite the strength of feeling from some Tory campaigners and senior politicians, and opposition parties.

The Conservative peer Sayeeda Warsi said on X: “The comments about Abbott are appalling, need to be condemned by the PM and the donation returned. Elections fought on the money of donors who make racist and offensive statements makes for dangerous election campaigns.”

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Kwarteng, who served as Britain’s first black chancellor under Liz Truss, said the remarks were “clearly” racist and sexist, noting: “I think Diane was right to point out the call to violence, even in a flippant way, is really inappropriate.”

Lord Hague said on Times Radio that Hester’s comments “do seem to be racist”, adding, “the comment, connecting dislike of Diane Abbott with racial characteristics – well, that is racist”.

Labour, the Liberal Democrats, the Green party and the Scottish National party have all criticised Hester’s comments.

On Tuesday, Starmer told ITV’s Lorraine: “The comments about Diane Abbott are just abhorrent. And Diane has been a trailblazer. She has paved the way for others, she’s probably faced more abuse than any other politician over the years on a sustained basis.

“And I’m sorry, this apology this morning that is pretending that what was said wasn’t racist or anything to do with the fact she’s a woman, I don’t buy that I’m afraid, and I think that it’s time the Tory party called it out and returned the money.”

Anneliese Dodds, the Labour party chair, said the Tories must “apologise unequivocally to Diane Abbott” and pay back Hester’s donations after Rishi Sunak conceded his alleged remarks were racist.

“After finally conceding that his comments are racist, what further proof does Rishi Sunak need that the Conservatives accepting Frank Hester’s cash is completely wrong?” she said.

No 10 had previously stopped short of describing comments made by Lee Anderson, the former Tory MP, as racist when he said Islamists had “got control” of the London mayor, Sadiq Khan, who is Muslim.

Anderson was ultimately stripped of the Conservative whip for failing to apologise for the interview on GB News, and he has now defected to the Reform party.