Boris Johnson has contacted Labour’s deputy leader Angela Rayner to make clear that he views claims about her in a Sunday newspaper misogynistic.
Politicians have condemned the suggestion Ms Rayner tries to distract the prime minister in the Commons by crossing and uncrossing her legs.
The Mail on Sunday said some unnamed Conservative MPs had made the claim.
A minister said Tory MPs who hold those views could face “serious consequences” if they were identified.
Technology minister Chris Philp told the BBC he expected the Conservative Party would attempt to “identify who was responsible for those views”, but said he doubted the Mail on Sunday would reveal who made those comments, given “journalists fiercely guard their sources”.
Downing Street will not be asking for an inquiry into who made the comments to the newspaper, with a source saying this was because such inquiries rarely found the person in question.
Ms Rayner dismissed the story as a “perverted smear” that showed women in politics faced misogyny every day.
On Sunday Mr Johnson criticised the comments tweeting: “As much as I disagree with Angela Rayner on almost every political issue, I respect her as a parliamentarian and deplore the misogyny directed at her anonymously today.”
A Downing Street source confirmed to the BBC that the prime minister had contacted Ms Rayner privately by text message to reiterate what he said in his public tweet.
BBC chief political correspondent Adam Fleming said that the texts between the two were in their “inimitable” styles, according to a source.
Shadow chancellor Rachel Reeves told BBC Breakfast that “instead of just tweeting, the prime minister needs to get his house in order” and ensure that his MPs did not think they had “carte blanche to be saying this sort of thing”.
“This is endemic,” she added, saying that she did not think there was a single female MP or staff member in the House of Commons who did not have their own stories of misogyny or sexism.
She told BBC Radio 4’s Today programme the claims were “absolutely outrageous”, and said it was indicative of a wider issue in Parliament.
“To be honest I am sick and tired of the way that female MPs and women are treated in Parliament and if this story and this outrageous slur on Angela gets things changed that would be a good thing.”
A raft of politicians, including female Tory MPs, have also spoken out in support of Ms Rayner.
Conservative Caroline Nokes said too many female MPs of all parties had been “on receiving end of vile articles”, while former minister Andrea Leadsom tweeted: “Really sorry Angela. Totally unacceptable comments and reporting.”
Labour leader Sir Keir Starmer said: “The sexism and misogyny peddled by the Tories is a disgraceful new low from a party mired in scandal and chaos.”
The Mail on Sunday is not commenting.
The article – which has now been changed to headline on deputy Labour leader Ms Rayner’s response on Twitter – quoted unnamed Conservative MPs claiming she would cross and uncross her legs when opposite the PM at the dispatch box in the Commons to distract him.
Many MPs have since also condemned the tone of the newspaper’s reporting.
And Ms Nokes – who chairs the women and equalities committee – confirmed on Twitter that she had contacted the Commons Speaker, Sir Lindsay Hoyle, to ask if the political editor who wrote the piece should have a press pass for Parliament.
The newspaper article said: “Tory MPs have mischievously suggested that Ms Rayner likes to distract the PM when he is in the dispatch box by deploying a fully-clothed Parliamentary equivalent of Sharon Stone’s infamous scene in the 1992 film Basic Instinct.”
The paper added: “It is also suggested she employs the tactic when sitting next to Sir Keir when he faces Mr Johnson at PMQs.”
The piece quotes one MP as saying: “She knows she can’t compete with Boris’s Oxford Union debating training, but she has other skills which he lacks.
“She has admitted as much when enjoying drinks with us on the [Commons] terrace.”
The article also described the Labour MP’s background as “a socialist grandmother who left school at 16 while pregnant and with no qualifications before becoming a care worker”.
She added: “I won’t be letting their vile lies deter me. Their attempts to harass and intimidate me will fail.
“I hope this experience doesn’t put off a single person like me, with a background like mine from aspiring to participate in public life. That would break my heart.”
The report led to support for the Labour deputy leader, with Scotland’s First Minister and SNP leader Nicola Sturgeon tweeting: “Solidarity from across the political divide to Angela Rayner on this.
“It’s a reminder of the deep misogyny women face every day.”
Liberal Democrat MP Munira Wilson described it as a “disgraceful story”, saying: “I can’t even believe it made it into print.”