May has ordered an investigation into an allegation that Damian Green, her de facto deputy and an old university friend, touched the woman's knee and sent her a suggestive text message before he joined the cabinet.
Green said it was "absolutely and completely untrue that I've ever made any sexual advances" towards journalist and Conservative activist Kate Maltby, who is 30 years younger than him.
"This untrue allegation has come as a complete shock and is deeply hurtful, especially from someone I considered a personal friend," he said.
A Downing Street spokesman said May had asked the head of the civil service, Jeremy Heywood, to "establish the facts and report back as soon as possible".
Allegations of sexual harassment and abuse have been circulating in Westminster for almost a week, with all party leaders pledging to do more to tackle what many admit is a pervasive problem.
In the most serious case, an opposition Labour party activist on Tuesday revealed she had been raped by a party member as a teenager six years ago -- but was told by a senior member of staff not to report it because it might harm her career.
Ministerial code probe
A list of MPs in May's Conservative party has also been circulated detailing ordinary relationships, sexual penchants and unspecified and unverified claims of inappropriate behaviour.
Among them is junior trade minister Mark Garnier, who is currently under investigation for breaches of the ministerial code for asking his then secretary to buy him sex toys in 2010.
Defence Secretary Michael Fallon has also apologised for putting his hand on a journalist's knee in 2002, but will face no investigation as the woman in question has brushed it off.
Maltby wrote in The Times on Wednesday how Green, a contact she met through her parents, put a "fleeting hand against my knee" when they went for a drink in early 2015.
"I had felt a meaningful political relationship was developing -- suddenly, I'd been made aware that there might be a price I was not prepared to pay," she wrote.
She cut off contact but Green sent her a text in May last year after she appeared in a magazine article wearing a corset, saying he had "admired" the picture and asking her if she wanted to meet for a drink.
Green said the text was sent in the spirit of "two friends agreeing to meet up for a regular catch-up".
She ignored it but got in touch when he was appointed to May's cabinet a few weeks later, and said they have since exchanged "many texts about political gossip".
