Boris Johnson has denied an allegation that he squeezed the thigh of a female journalist under the table during a private lunch.
Charlotte Edwardes said the incident took place at the offices of The Spectator magazine in London shortly after Mr Johnson became editor in 1999.
Asked if he had done it, the prime minister said: "No, and I think what the public want to hear is about what we are doing to level up and unite the country."
Asked if she had made it up, he said: "I'm just saying what I've said. What the public want to hear is what we are doing for them and for the country and the investment in ways of uniting the country."
Ms Edwardes had said that after the lunch, she had confided in the young woman who was sitting on the other side of Mr Johnson, who told her: "Oh God, he did exactly the same to me."
In another twist, the wife of the prime minister’s senior adviser Dominic Cummings has issued a statement insisting she is not the other woman mentioned by Ms Edwardes.
Spectator magazine commissioning editor Mary Wakefield said: "I am not the woman referred to in Charlotte Edwardes's column.
Statement from my colleague @MaryWakefield 'I am not the woman referred to in Charlotte Edwardes’s column. Boris was a good boss and nothing like this ever happened to me. Nor has Charlotte, who I like and admire, ever discussed the incident with me.'— James Forsyth (@JGForsyth) September 30, 2019
"Boris was a good boss and nothing like this ever happened to me. Nor has Charlotte, who I like and admire, ever discussed the incident with me."
The statement was tweeted by Spectator political editor James Forsyth.
Earlier, a Number 10 spokesman said of Ms Edwardes’s claim: "This allegation is untrue."
It comes as the police watchdog decides whether or not to investigate the Prime Minister over his links to the American businesswoman Jennifer Arcuri.
A poll last week revealed that Mr Johnson’s popularity among women has declined since the end of August.
Despite the Number 10 denial, senior Conservatives – including a member of Mr Johnson's Cabinet – said Ms Edwardes was trustworthy.
Ms Edwardes herself added: "If the prime minister doesn't recollect the incident then clearly I have a better memory than he does."
If the prime minister doesn’t recollect the incident then clearly I have a better memory than he does https://t.co/pbcLJThkqP— Charlotte Edwardes (@chedwardes) September 29, 2019
Health Secretary Matt Hancock, who said he knows Ms Edwardes well, said he believed her to be trustworthy, adding: "I entirely trust what she has to say."
Asked if he believed her claims, he said: "I know her and I know her to be trustworthy."
Former work and pensions secretary Amber Rudd said in a tweet: "I agree with @MattHancock".
Chancellor Sajid Javid told BBC Radio 4's Today programme that Mr Johnson had his support.
"I've talked to the prime minster about that and, first of all, he couldn't be clearer, absolutely clear, that they are completely untrue and I totally trust him in that,” he said.
When asked if Mr Johnson has a “woman problem”, Mr Javid said: “No, not at all.”
Writing in her first column for The Sunday Times, Ms Edwardes said: "I'm seated on Johnson's right; on his left is a young woman I know.
"More wine is poured; more wine is drunk. Under the table I feel Johnson's hand on my thigh. He gives it a squeeze.
"His hand is high up my leg and he has enough inner flesh beneath his fingers to make me sit suddenly upright."
Labour's shadow secretary for women and equalities Dawn Butler said it was a "shocking but sadly all too familiar story".
She tweeted: "What is it about powerful men feeling entitled to harass women? Boris Johnson has serious questions to answer.”
The allegations were made at the start of the Conservative Party conference in Manchester.
Earlier, Mr Hancock had played down the report, saying there were "always lots of other stories in papers".
Speaking at a Tory party fringe event in Manchester hosted by HuffPostUK, he said: "Boris has never lectured other people about their private lives.
"I think that we should concentrate on delivering on what we are in politics for, which in my view is to serve the citizens of this country."
But speaking to Channel 4 News, Mr Hancock said he did not "dismiss it at all".
Mr Hancock said he did not know the details, saying it was incumbent not to "react without the full details". He added: "I know Charlotte well, and I entirely trust what she has to say."
Mr Hancock said: "What I would say is that these are important issues and getting the response right is incredibly important.
"But there's also something here about making sure that the way I try to carry on my life – both in public and in private, frankly – is with a high degree of integrity."
He added: "Nobody's perfect but I think that is how we should try to go about things."