The prime minister said Usman Khan, who was freed halfway through a 16-year jail sentence, was on the streets because of laws introduced by a “leftie government”.
He described the release of criminals who are “as dangerous as this man” as “repulsive” and vowed to take steps to ensure people are not released early when they commit serious offences.
But Labour leader Jeremy Corbyn said convicted terrorists should “not necessarily” serve their full prison sentence while shadow attorney general Shami Chakrabarti claimed it was “unedifying” to talk about “throwing away the keys”.
The Liberal Democrats, meanwhile, criticised the two main parties for seeking to use the incident as a “political football”.
On Saturday night, David Merritt said his son Jack, who was killed in the attack, would “not wish his death to be used as the pretext for more draconian sentences or for detaining people unnecessarily”.
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.
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.