But a spokesman Mr Corbyn denied he had said "stupid woman", instead insisting he had mouthed "stupid people", referring generally to MPs.
And Health Secretary Matt Hancock added: "The mask slips".
May delayed a crucial parliamentary vote on her withdrawal deal last week as it faced nearly certain defeat in the House of Commons.
The reaction to Corbyn's insult has been mixed.
He said that Mr Corbyn would be willing to repeat his denial in the Commons chamber.
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The Daily Telegraph says the Labour leader was accused of sexism as a Commons session descended into farce, with Parliament spending more than an hour arguing over whether he had uttered the phrase.
British opposition leader Jeremy Corbyn got himself into trouble on Wednesday (Dec 19) for apparently muttering "stupid woman" at Prime Minister Theresa May during a heated exchange in parliament over her delaying tactics on Brexit.
The intervention came as Diane Abbott tried to shrug off mounting fury by arguing "nobody knows" what he really said, and accusing MPs of "confected" rage.
It brought condemnation from Tory MPs, with party chairman Brandon Lewis urging him to either "apologise or clarify" what he had mouthed.
"I did not use the words "stupid woman" about the Prime Minister or anyone else, and am completely opposed to the use of sexist or misogynist language in absolutely any form at all", Corbyn said. "People who are trying to make out he said something he didn't have to account for themselves".
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Asked by a BBC reporter in Northampton, where he was visiting a homeless shelter, whether he had used respectful language, Mr Corbyn said: "I muttered it to myself, actually, in Parliament, and you and your colleagues in the media seem utterly obsessed with this".
She said: "This is just the latest in a long line of misogynistic behaviour from Corbyn and his top team".
In an accompanying video, Mr Corbyn said: "Yesterday the Tories tried to turn parliament into a pantomime, tried to turn it into a pantomime when there are very serious issues".
"The attempt to drive up the risk of a no deal or to give that impression is designed to create a false choice between no deal and her deal".
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