Mr Johnson said the attack, which left two people dead and three injured, was the result of a decision by a “leftie government” and pledged to change the law on automatic release of prisoners.
His comments came after a plea by the family of one of the victims, Jack Merritt, that his death not be used politically.
She added that the interview had served only to answer the question of why Mr Johnson was “so desperate to avoid detailed scrutiny in this campaign”.
Her Westminster leader Ian Blackford went further, saying: “Boris Johnson is utterly unfit to be Prime Minister. On policy, on leadership and on personal character, Scotland deserves better.”
Mr Johnson has come under sustained criticism for not agreeing to be interviewed by the BBC’s Andrew Neil, unlike the other party leaders, and he also failed to appear on a Channel 4 leaders’ debate last week.
However, he did appear on television yesterday to respond to Friday’s attack in which 28-year-old terrorist Usman Khan, who was freed halfway through a 16-year jail sentence, was shot dead after he stabbed 25-year-old Mr Merrit and 23-year-old Saskia Jones to death.
PM blames Labour
Mr Johnson said it was both “ridiculous” and “repulsive” that “individuals as dangerous as this man should be allowed out after serving only eight years”, and placed the blame for Khan’s release on Labour, saying: “His release was necessary under the law because of the automatic early release scheme under which he was sentenced. That was the reality, and that was brought in by Labour with the support of Jeremy Corbyn and the rest of the Labour Party.
“I opposed it both in 2003 and 2008, and now that I am Prime Minister I’m going to take steps to make sure that people are not released early when they commit... serious sexual, violent or terrorist offences.”
He added: “The reason this killer was out on the streets was because of automatic early release, which was brought in by a leftie government.”
David Merritt said his son’s death should not be used to score political points. He said: “We know Jack would not want this terrible, isolated incident to be used as a pretext by the government for introducing even more draconian sentences on prisoners or for detaining people in prison for longer than necessary.”
Khan was on licence and wearing an electronic monitoring tag when he attended a conference on prisoner rehabilitation hosted by Cambridge University scheme Learning Together at Fishmongers’ Hall, near London Bridge.
Mr Merritt was the course coordinator of the university’s programme and Ms Jones was attending the programme as a volunteer.
Armed with two knives and wearing a fake suicide vest, Khan was tackled by members of the public before he was shot dead by police on London Bridge. Online footage shows one man spraying him with a fire extinguisher and another lunging at him with a narwhal tusk believed to have been taken from the wall inside the building.
The attack prompted the Ministry of Justice to review the licence conditions of every convicted terrorist released from prison.
Mr Johnson added: “We’ve taken a lot of action, as you can imagine, in the last 48 hours. I’m sure people can imagine what we’re doing to ensure that 74 other individuals who’ve been let out early on the basis of this Labour change in legislation – they are being properly invigilated to make sure there is no threat.”
Pressed on cuts to prison and probation services, 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.”
Labour leader Jeremy Corbyn said neither the parole board nor probation service had been involved with Khan, which required investigatin