Mr Corbyn has been forced to backtrack on his calls for Theresa May to “resign immediately”
The Labour leader faced an embarrassing climbdown after demanding the Prime Minister quit over her record as home secretary when police numbers fell by almost 20,000.
He was asked in an interview this afternoon whether he thought Mrs May should resign and said meekly: “No.”
Hours earlier, Mr Corbyn had said in an interview that Mrs May should stand down.
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."
But he quickly changed his tune after he received condemnation for his remarks.
The politicians also sparred over Saturday night's murderous rampage by three terrorists in the heart of London.
Liberal Democrat leader Tim Farron also accused Mrs May of failing in her duty to keep the UK safe
The attackers slashed people's throats from behind while victims endured violence so horrific they were left unable to speak, according to accounts emerging two days later.
The terrorists first rammed a van into pedestrians at high speed on London Bridge, before running into narrow streets buzzing with nightlife in the Borough Market area and stabbing people indiscriminately with long knives.
The attack left seven people dead and 48 injured, of whom 18 were still in a critical condition on Monday. The terrorists were shot dead by armed police.
Theresa May responsible for security failures of London Bridge, Manchester, Westminster Bridge. Should be resigning not seeking re-election pic.twitter.com/2o0odey2BQ
— steve hilton (@SteveHiltonx) June 5, 2017
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In the wake of the attack, Mrs May defended her record as the Tories hit out at Labour over Mr Corbyn's record on tackling terrorism.
The Conservative Party's official Twitter account said "the shoot-to-kill policy saves British lives – Jeremy Corbyn opposes it".
Mr Corbyn insisted his comments on shoot-to-kill had been taken out of context and he backed the police to take the "necessary action" where lives were at risk.
Steve Hilton,said Mrs May was "responsible for security failures"
He said: "What I said was that I wanted our police to be able to act in a defensive capacity. I don't want anybody, nobody wants police going out shooting people.
"They don't want to do it, nobody wants to do it. In the situation that they were faced (with) at the weekend or faced in Westminster, they took the necessary action."
Mr Corbyn’s initial calls for Mrs May had come after Steve Hilton, a former adviser to David Cameron in Number 10, said Mrs May was "responsible for security failures" and "should be resigning, not seeking re-election".
Yet, the Labour leader later clarified his views, stressing it was a matter for the electorate whether to oust Mrs May: "I'm not backing away from anything, what I'm saying is there's an election on now there's a choice before everybody.
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"I'm articulating what is a deep anger amongst those people that have seen 20,000 police officers lose their jobs, seen firefighters lose their jobs, seen ambulance crews unable to cope.
“[Mrs May] needs to think about what she did while she was home secretary."
However, Liberal Democrat leader Tim Farron also accused Mrs May of failing in her duty to keep the UK safe.
He told the Press Association: "On one of the most important tests facing us as a country – security – Theresa May has failed as both prime minister and home secretary. She has failed by cutting police numbers.
"She has made poor choices. She has chosen to give away a corporation tax cut to the biggest and wealthiest businesses in our country, multi-nationals, instead of spending that money on keeping us safe and backing the police force and security services.
Disastrous moment Jeremy Corbyn’s car ran over a BBC cameraman’s foot Thu, May 11, 2017 Play slideshow Getty Images 1 of 9
Jeremy Corbyn looks around as he arrives at Savoy Place
"Cutting police numbers is the most sure way of keeping us less safe."
Facing repeated questions about her record after a speech in London, Mrs May said: "I have been responsible for giving the police extra powers to deal with terrorism.
"Jeremy Corbyn has boasted that he has opposed those powers and opposed the powers for anti-terror actions throughout his time in Parliament.
"And I also support, absolutely, shoot-to-kill and I think what we saw on our streets on Saturday was how important that was."
She said that since 2015 police budgets had been protected "despite the fact that Jeremy Corbyn's front bench suggested that police budgets should be cut by up to 10 per cent".
Mrs May was giving a speech at the Royal United Services Institute, where she had launched her campaign for the Tory leadership just under a year ago.