Mr Khan was taking part in a phone-in on LBC Radio on Thursday lunchtime, where he answered questions from the general public.
He told one caller: “The party has not responded to serious concerns of antisemitism the way the Labour party should have done.
“I think the Labour party has fallen woefully short and we should apologise, not to the Jewish community, but everybody for the way out party has failed to get a grip with this problem.”
Continuing, Mr Khan said: “Jeremy Corbyn has spent his entire life being an anti-racist campaigner, whether it’s apartheid in South Africa or racism in this country - and that does include anti-semitism.”
Mr Khan then took aim at the Prime Minister - who he claims was on record saying far more racist and Islamophobic things than the Labour leader.
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Mr Khan said: “I can point to things on the record that the alternative candidate, Boris Johnson, has said about people of colour and of different faiths, on the record. Overtly, proudly... been paid for it.
“You point to examples where Jeremy Corbyn has said things on the record, in articles, in speeches, for a cheap joke, about people of different colour and faith.
“If you’re having a scales, Boris Johnson has said far and done far more outrageous - and in my view - racist things than Jeremy Corbyn.
“Do I think he is a good leader? Hand on heart, yeah. And I will be campaigning tonight and over the course of the next seven days to get as many Labour MPs to return to Parliament.
“Because the choice is a Government that backs Brexit, that loves austerity and a Government that will give the public a final say on Brexit and will end austerity once and for all.”
The Mayor also answered questions on issues such as Uber’s London licence ban, accusations of antisemitism within the Labour Party, the London Bridge terror attack and the leadership debate in the run up to the December 12 General Election.
Yahoo News UK has contacted the Conservative Party for comment.