The wife of the PM’s chief adviser, Mary Wakefield, says Boris Johnson did not touch her thigh at a lunch in 1999.
Charlotte Edwardes has accused Mr Johnson of touching her under the table and said he touched a second woman too.
The BBC’s Laura Kuenssberg said a rumour had been circulating at the Conservative conference that Ms Wakefield was the other woman involved, but she has denied it.
The PM has also denied Ms Edwardes’ allegation, made in the Sunday Times.
In a statement, Ms Wakefield, who is married to Dominic Cummings, said “nothing like this ever happened to me”.
Earlier, ex-Tory minister Justine Greening said Ms Edwardes’ story was “deeply concerning”, but Chancellor Sajid Javid said he had “full faith” in the PM.
On Sunday evening, No 10 released a statement calling the claims “untrue”, but Ms Edwardes later tweeted: “If the prime minister doesn’t recollect the incident then clearly I have a better memory than he does.”
Asked on Monday if the incident had taken place, Mr Johnson said: “No.”
He also denied it had overshadowed the Conservative Party conference taking place in Manchester this week.
In her first column for the Sunday Times, Ms Edwardes said the incident took place in 1999. Ms Edwardes said she was seated on Mr Johnson’s right at the lunch, held at the Spectator magazine’s offices.
Mr Johnson was editor of the magazine at the time.
“More wine is poured; more wine is drunk. Under the table I feel Johnson’s hand on my thigh. He gives it a squeeze,” she wrote.
“His hand is high up my leg and he has enough inner flesh beneath his fingers to make me sit suddenly upright.”
Ms Edwardes said another woman at the lunch later told her he had done the same to her.
Spectator magazine commissioning editor Ms Wakefield issued a statement to say she was “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.”
Mr Javid refused to comment on the “personal allegations” against the PM when asked on BBC Breakfast, adding: “The prime minister has said that this is completely untrue.
“I have full faith in the prime minister and I don’t doubt that and what he has said for a second.”
However, Ms Greening told BBC Radio 4’s Today programme: “I can’t comment on those accusations, but they are deeply concerning, and in a sense they go to the heart of this question about character and integrity of people in public life and what standards the electorate have a right to expect.”
At a conference fringe event on Sunday lunchtime, Health Secretary Matt Hancock appeared to play down the claims.
He said Mr Johnson “has never lectured other people about their private lives,” adding: “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.”
Later, though, in an interview with Channel 4 News – conducted before No 10 issued its denial – Mr Hancock stressed that he did not intend to make light of Ms Edwardes’ allegations.
“I don’t dismiss it at all. I have seen how what I said has been… how people have responded to what I said, and [to be] totally clear about it, these issues are incredibly important.”
He said he knew Ms Edwardes well and knew her to be “trustworthy”.
Former minister Amber Rudd – who quit the Conservative Party over its handling of Brexit earlier this month – tweeted that she agreed with Mr Hancock’s conclusion.
But Housing Secretary Robert Jenrick said, unless further evidence emerged, he would “take [the prime minister] at his word”.
“I don’t have any inside information into this,” he told BBC Politics Live.
“It’s very hard for any of us to speculate on what may or may not have happened.”
Dominic Cummings’ wife rejects Boris Johnson ‘touching’ report}