An off-duty policeman injured as he tried to fend off the London Bridge terrorists "would no doubt do exactly the same again", his family said.
Pc Charlie Guenigault was said to have taken on the knife-wielding attackers with his bare hands, leaving him badly injured.
In a statement, his family said they were "extremely proud" of his "immense bravery" in facing down the killers on Saturday night.
They said: "Given the opportunity again, Charlie would no doubt do exactly the same if faced with the same situation; helping a fellow police officer in need and protecting the public."
The 25-year-old officer is still recovering in hospital, but is now in a stable condition, police said.
A member of the Metropolitan Police's emergency response team based in Southwark borough, the constable had been enjoying a drink after work when the attackers began their rampage.
The family statement said: "We are extremely proud of Charlie who showed immense bravery on Saturday night.
"Our family has received numerous messages from friends, colleagues and people around the country sending Charlie good wishes and commending him for his actions.
"We are very grateful for this and it has provided us with a lot of comfort at this difficult time.
"He is immensely proud to work for the Metropolitan Police Service and serving the Southwark community, and this is an example of that.
"Charlie is described by his peers as a dedicated police officer, who is a diligent, hardworking and respected member of his team.
"We would ask for privacy at this time as we concentrate on Charlie's recovery."
On Monday, Metropolitan Police Commissioner Cressida Dick said she was "enormously proud" of Mr Guenigault, who stepped in to help uniformed colleagues and members of the public.
"He had finished a day's work and was having a drink with friends and he witnessed the attack," she told BBC Breakfast.
"My understanding is that, without hesitation, wearing his normal clothes, he dived in and tried to assist, and he I'm afraid was himself severely injured, but utterly heroic."