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.
Full article -
Angela Rayner: Tory source of misogyny claims will be punished, Boris Johnson says