The left-wing politician attacked his rival in the upcoming General Election over Government cuts which had left the police with 20,000 fewer officers than in 2010.
Asked by ITV News if he would back calls for Theresa May to resign, he said: "Indeed I would, because there's been calls made by a lot of very responsible people on this who are very worried that she was at the Home Office for all this time, presided over these cuts in police numbers and is now saying that we have a problem – yes, we do have a problem, we should never have cut the police numbers."
In the aftermath of the London Bridge terror attack, which saw three men kill seven people and injure 48, 21 of whom are in a critical condition, in just eight minutes, Mrs May has come under pressure for her record as Home Secretary.
Labour leader Jeremy Corbyn has called for Theresa May to resign
Prime Minister Theresa May faced calls for her to resign from Jeremy Corbyn
The Labour leader accused Mrs May of trying to “protect the public on the cheap” by cutting police numbers, despite a Police Federation warning over public safety.
A Labour spokesman said: "Jeremy is saying he believes the public will judge her on her record.
“We have an election on Thursday where there is an opportunity to vote in a Labour government for the many not the few, one that will invest in police and security services rather than cut them.”
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David Cameron's former aide Steve Hilton, who was the former Prime Minister’s Strategy Director, has also called for Mrs May to go and said she should have taken responsibility for the cuts she made while at the Home Office.
Mr Hilton wrote on Twitter: "Theresa May responsible for security failures of London Bridge, Manchester, Westminster Bridge.
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"Should be resigning not seeking re-election.
"Theresa May blame-shifting again. Her spin doctors attack MI5, but she was in charge of them for years."
David Cameron's former aide Steve Hilton has also called for Theresa May to resign
Mrs May said: "The Commissioner of the Metropolitan Police has said that the Met is well-resourced, and they are, and that they have very powerful counter-terrorism capabilities, and they do, we have protected counter-terrorism policing budgets.
"We have also provided funding for an increase in the number of armed police officers since 2015. We have protected our all police budgets."
The row came as the head of Scotland Yard Cressida Dick said "of course" it was right to look at police resources in light of the recent attacks.
Labour says the cut in officer numbers, by around 20,000 since the Tories took power, made it harder for community police to nip potential extremism in the bud.