Video report by ITV News Correspondent Neil Connery
The family of the London Bridge terrorist Usman Khan said they are "saddened and shocked" by the atrocity and "totally condemn his actions".
In a short statement issued through the Metropolitan Police, they expressed their condolences to the two victims who died and those who were injured in the violence on Friday.
It read: "We are saddened and shocked by what Usman has done. We totally condemn his actions and we wish to express our condolences to the families of the victims that have died and wish a speedy recovery to all of the injured.
"We would like to request privacy for our family at this difficult time."
Cambridge University graduates Jack Merritt, 25, and Saskia Jones, 23, were both stabbed to death by the 28-year-old convicted terrorist during a prisoner rehabilitation event they were supporting at London’s Fishmongers’ Hall.
On Monday, the family of Mr Merritt gathered to pay tribute to him and Miss Jones at a service in Cambridge, in which his girlfriend Leanne O’Brien was seen breaking down in tears.
She also posted the message on Facebook after Mr Merritt’s father David attacked politicians for using his son’s death "to perpetuate an agenda of hate".
She wrote of her boyfriend: "My love, you are phenomenal and have opened so many doors for those that society turned their backs on."
"He would be seething at his death, and his life, being used to perpetuate an agenda of hate that he gave his everything fighting against," he said.
"What Jack would want from this is for all of us to walk through the door he has booted down, in his black Doc Martens," he added.
It came after Boris Johnson sought to blame Labour for the early release of the convicted terrorist as the political row over the knife attack intensified.
Khan, who was living in Stafford, was given permission to travel into the heart of London by police and the probation service.
Convicted of planning to bomb the London Stock Exchange in February 2012, he was released from prison on licence in December 2018, halfway through his 16-year prison sentence.
He launched the fatal attack at an event held by Learning Together, a programme associated with the university’s Institute of Criminology, at Fishmongers’ Hall near London Bridge.
Armed with two knives and wearing a fake suicide vest, he was tackled by members of the public, including ex-offenders from the conference, before he was shot dead by police.
One of the three people injured in the attack has been allowed to return home while the other two remain in a stable condition in hospital, Met Police said.
No-one else is being sought over the attack.