Mrs May accused the Labour leader of not opening his eyes to antisemitism following months of mounting criticism over his handling of the issue.
During Prime Minister’s Questions, she held up an advert in the Guardian newspaper taken out by more than 60 Labour peers which criticises Mr Corbyn for a “toxic culture you have allowed to divide our movement”.
Mrs May told the Commons that the Labour leader “needs to apologise for his failure to deal with racism in the Labour Party”.
The advert accuses Mr Corbyn of “failing the test of leadership” and blames him for a “toxic culture you have allowed to divide our movement” that has prompted the resignation of “thousands” of members.
The party, peers claimed, is no longer a “safe place” for its members and supporters.
The advert was backed by 67 Labour peers including Peter Hain, Peter Mandelson and Robert Winston, as well as senior Scottish peers George Robertson and George Foulkes.
Lord Robertson told the Evening Standard that Mr Corbyn had to show “anger and shame” to heal the wounds within the party. At PMQs, Mr Corbyn insisted Labour “totally opposes” racism in all its forms and hit back at the PM over Islamophobia within Conservative ranks.
He said: “This party totally opposes racism in any form whatsoever. Antisemitism has no place in our society, no place in any of our parties, and no place in any of our dialogue. Neither does any other form of racism.
“When 60 per cent of Tory Party members think Islam is a threat to western civilisation... I look forward to that being dealt with as we deal with any racism that occurs within our own party as well.”
Earlier, shadow Chancellor John McDonnell said he would listen to the views of the Labour peers.
He said: “We’ll listen to their views. I’m not sure why they’ve put an advert in the Guardian – they could have just written to us or popped in for a meeting. But we’ll listen to them.”
Mr McDonnell insisted Labour is a “safe place for Jewish people”.
A Labour spokesman suggested that there should be resignations over a BBC Panorama programme that alleged interference by Mr Corbyn’s office in complaints about antisemitism.
“There are serious factual errors, an almost extraordinary lack of balance in the way the programme was put together,” Mr Corbyn’s spokesman said.
They alleged a “complete lack of signposting about what was being reported, the political creations of those involved, the editing of emails to give them the opposite meaning, the invention of quotes”.