The article said some unnamed Tory MPs claimed Labour’s deputy leader tried to distract Boris Johnson by crossing and uncrossing her legs in Parliament.
The story and the tone of the piece has been widely condemned, with the PM calling it “sexist tripe”.
Editor David Dillon said journalists should decide what to report.
He rejected Sir Lindsay Hoyle’s invitation to discuss the piece, published in the paper at the weekend on page five.
After its publication it was criticised from across the political divide as being misogynistic and the UK press regulator Ipso has received thousands of complaints.
The piece said: “Tory MPs have mischievously suggested that Ms Rayner likes to distract the PM when he is in the despatch box by deploying a fully clothed parliamentary equivalent of Sharon Stone’s infamous scene in the 1992 film Basic Instinct.”
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It quoted an unnamed Conservative MP saying Ms Rayner “knows she can’t compete with Boris’s Oxford Union debating training, but she has other skills which he lacks”.
Ms Rayner said she was crestfallen over the story and that women in politics “face sexism and misogyny every day”.
She also accused the article of being “steeped in classism”, suggesting she was “thick” as she had attended a comprehensive school, and insinuated she was “promiscuous” for having a child aged 16.
Mr Johnson said he respected Ms Rayner as a parliamentarian and “deplored the misogyny” in the piece, while Labour leader Sir Keir Starmer called it a “disgraceful new low” for the Conservative Party.
In response to the invite, The Mail’s front page headline on Wednesday reads: “No Mister Speaker: In the name of a free press, The Mail respectfully declines the Commons Speaker’s summons…”
Sir Lindsay Hoyle seen in the Speaker’s chair in the House of Commons
IMAGE SOURCE,PA MEDIA
Speaking in the House on Monday, Sir Lindsay called the story “misogynistic and offensive” and said he was arranging a meeting with Mr Dillon and the Mail on Sunday’s political editor, Glen Owen, whose name appeared next to the story.
In a letter on Tuesday, Mr Dillon said he had initially intended to attend the meeting “to draw a line under matters”, but that Sir Lindsay’s comments in the Commons indicated he had already “passed judgment on our article”.
“The Mail on Sunday deplores sexism and misogyny in all its forms,” Mr Dillon wrote.
“However, journalists must be free to report what they are told by MPs about conversations which take place in the House of Commons, however unpalatable some may find them.”
He added that the freedom of the press would “not last if journalists have to take instruction from officials of the House of Commons, however august they may be, on what they can report and not report”.
The newspaper also pointed to a interview in which Ms Rayner had laughed about the Basic Instinct comparison.
Speaking to Matt Forde’s The Political Party podcast in January, she added she was “mortified” by suggestions on the internet that she was using her body to distract the prime minister saying: “I don’t need to do that.”
Sir Lindsay earlier said he was a “staunch believer and protector of press freedom” and that he “firmly [believed] in the duty of reporters to cover Parliament”.
He said he had wanted to use the meeting to “make a plea – nothing more – for the feelings of all MPs and their families to be considered, and the impact on their safety, when articles are written”.
The UK press regulator Ipso has said it is exploring possible breaches of its code of practice after receiving 5,500 complaints about the article.