Usman Khan, 28, was shot dead by police after stabbing several people in London Bridge at around 2:00 p.m. (GMT) on Friday.
He was released from prison in December 2018 after serving half of a 16-year sentence for planning to plant a bomb at the London Stock Exchange, Efe news reported.
"It does not make sense for us as a society to be putting people convicted of terrorist offences, of serious violent offences, out on early release," Conservative leader Johnson said during a visit to London Bridge on Saturday.
Johnson, who is leading the polls for the general elections slated for 12 December, added that the Conservative Party manifesto says his government would issue tougher sentences for serious and violent crimes.
"It is a mistake to allow serious and violent criminals to come out of prison early and it is very important that we get out of that habit and that we enforce the appropriate sentences for dangerous criminals, especially for terrorists," the PM said on Friday ahead of an emergency meeting with the government's Cobra committee.
Johnson reiterated his view when visiting the scene of the attack.
"Obviously it's early days and there's a lot of investigations that need to be done.
"But it is clear to me that this guy was out, he'd served half of his sentence.
"He was out on automatic early release and I have long said that this system simply isn't working," the prime minister added.
Johnson commended the rapid response of the police, who shot down the attacker five minutes after receiving the alert that a stabbing spree was taking place.
At the time of the attack, Khan had participated in a conference organised by the University of Cambridge on the reintegration of prisoners, in a building on the north end of London Bridge.
Before the police arrived, a group of civil managed to hold the attacker to the ground.
British media have revealed the men who challenged Khan were former offenders who had also been involved in the conference on reintegration, as well as a Polish-born chef.
One of the two people he killed was Jack Merritt, 25, coordinator of a reintegration program of the Institute of Criminology at Cambridge, British media reported.
The identity of the woman Khan killed has not yet been revealed. Three others were injured, one of whom is in a critical but stable state.
Meanwhile the Islamic State (IS) claimed responsibility on Saturday for Khan's lethal assault, according to the SITE consultancy that specializes in jihadist terrorism.
The author of yesterday's attack in London was an Islamic State combatant, SITE said in repeating a message from the Amaq News Agency, linked to terrorists and whose accounts on most social networks have been blocked over the last few days by the authorities.
( With inputs from IANS )