Theresa May has asked for Whitehall officials to investigate allegations that Damian Green made inappropriate advances towards a female activist.
Writing in The Times, Kate Maltby accused the First Secretary of State of "fleetingly" touching her knee during a 2015 meeting in a London pub, and of sending her a "suggestive" text two years later.
Green has denied the allegations, calling them "untrue” and “deeply hurtful".
Speaking outside his home on Wednesday, he said: "All the allegations are completely false."
The claims against Green are the latest in a swirl of rumours relating to sexual harassment by MPs.
Labour has launched an inquiry into claims an activist was discouraged by party officials from reporting an alleged rape at a Labour event in 2011.
In a case reported by ITV News, an anonymous woman claimed she was sexually assaulted by an MP on a foreign work trip last year, allegations that authorities ignored.
Maltby, 31, said Green, 61, was a friend of her parents who she approached for advice on political activism during her 20s.
She said they met for drinks in 2015, a meeting in which Green said he could help her if she wanted a political career, before turning to conversation to affairs at Westminster. Mentioning his wife was “very understanding,” Maltby claims she “felt a fleeting hand against my knee - so brief it was almost deniable."
Two years later, Maltby appeared in a newspaper photograph, promoting Green to text her saying he "admired you in a corset" and asking if she wanted to go for another drink.
Maltby said she ignored the message, but contacted him six weeks later to congratulate him on his appointment to the cabinet.
Malty said she doubted Green knew how "awkward, embarrassed and professionally compromised" she felt about the alleged touch.
Responding to the allegations, Green said: "It is absolutely and completely untrue that I've ever made any sexual advances on Maltby.
"I have known Ms Maltby since she contacted me as board member of Bright Blue, the Conservative think tank, in 2014, and we have had a drink as friends twice-yearly.
"The text I sent after she appeared in a newspaper article was sent in that spirit - as two friends agreeing to meet for a regular catch up - and nothing more.
"This untrue allegation has come as a complete shock and is deeply hurtful, especially from someone I considered a personal friend."
A Downing Street spokesman said: "An allegation has been made in relation to the First Secretary of State, which he strongly denies.
"The Prime Minister has referred the matter to the Cabinet Secretary to establish the facts and report back as soon as possible."