Video report by ITV News Correspondent Lucy Watson
As the political blame game continued over Friday’s attack, which has claimed two victims, Mr Johnson said killer Usman Khan was on the streets because of laws introduced by a “leftie government”.
Legal experts have contradicted Mr Johnson’s claims that laws related to automatic early release rendered Khan’s shortened sentence inevitable.
Earlier on Sunday, Mr Corbyn said police had no choice but to shoot Khan, who was freed halfway through a 16-year jail sentence, but argued the length of a terrorist’s sentence “depends on the circumstances”.
ITV News Political Correspondent Daniel Hewitt says the blame game is well under way
In an interview on BBC One’s The Andrew Marr Show, Mr Johnson said: “The reason this killer was out on the streets was because of automatic early release which was brought in by a leftie government.”
Pressed on cuts to prison and probation services and the rising levels of assaults on staff during this time, he added: “That is why this new Conservative administration is putting £2.5 billion into our prison service.”
Asked why this has not happened under the last years of Conservative government, he added: “I’m a new Prime Minister, we take a different approach.”
Mr Marr repeatedly reminded Mr Johnson the Conservatives have been in power for nearly ten years.
Mr Corbyn told Sky’s Sophy Ridge on Sunday that it “depends on the circumstances” and that it was “not necessarily” the case that people convicted of terrorism offences needed to serve a full prison sentence.
He said: “I think there has to be an examination of how our prison services work and crucially what happens to them on release from prison because I need to know whether or not the Parole Board were involved in his release, apparently they were not, they made that statement quite quickly after the release… after yesterday’s terrible incident.
“Secondly, there were apparently no probation service involvement in monitoring this former prisoner who after all had only served half his sentence and he came out I think a year ago and there has to be an examination of what goes on in the prison because prisons ought to be a place where people are put away because of major serious offences but also a place where rehabilitation takes place.”
Mr Corbyn said police were “stuck with a situation where there was a credible threat of a bomb belt around his body and it’s an awful situation for any police officer, any public servant to be put in” as he backed the decision to kill the attacker.
He later used a speech in York to criticise the cuts made to policing and the justice system as putting the country at risk, saying: "You cannot keep people safe on the cheap."
David Merritt, whose son Jack was killed by Khan on Friday, said: "My son, Jack, who was killed in this attack, would not wish his death to be used as the pretext for more draconian sentences or for detaining people unnecessarily."
The Liberal Democrats, meanwhile, criticised the two main parties for seeking to use the incident as a “political football”.
Leader Jo Swinson has accused Mr Johnson of trying to make Friday's terror attack an election issue, adding that his behaviour is "pretty distasteful".
Speaking on BBC Radio 5 Live's Pieenar's Politics, Ms Swinson said: "This was an opportunity for Boris Johnson to be a statesman and yet again he has failed in that and just shown why he is not fit for the job of Prime Minister.
"You've got a community which is coming together in a brilliant way and straight out of the door the Prime Minister's trying to make it an election issue - I just think it's pretty distasteful."