Without identifying the victims by name, Foreign Minister Julie Bishop confirmed that three Australians "have been affected".
"One is currently in hospital but she is recovering, and I have spoken to her father. Another man - who, I understand, received stitches - is on his way back to Australia. I believe he's been speaking to the media. And there is a third Australian. We're still making inquiries with respect to the circumstances of the third Australian," she told ABC Radio.
A Brisbane woman was badly wounded when one of the London terrorists slashed her throat in Saturday's deadly attack - she is one of three Australians caught up in the attack.
Father of Candice Hedge speaks of ordeal
Candice Hedge, 30, is recovering in St Thomas' Hospital in London.
"Hey everyone, just so you know im doing ok. Bit of pain but I will survive. Thanks for your thoughts and well wishes. Love to all," she said in a Facebook post.
It's been reported that one of the terrorists pulled back her head and slashed her throat, but missed her windpipe and arteries.
She's one of three Australians known to have been caught up in the deadly rampage that started on London Bridge and ended in the bar and restaurant district of Burough Market.
A second person has been named as Darwin man Andrew Morrison by Newscorp papers.
“He got me but I dodged it, I ducked and weaved," he says in a video posted to social media, holding a bloodied piece of material to his neck.
"I push him off. I walk into a pub and say 'Someone help me - I've been stabbed,'" he said.
Theresa May calls to ramp up counter-terrorism
Canadian and French victims among those killed
Governments in Canada and France have confirmed that each country had a citizen who was killed in the attack.
The first named fatality was Chrissy Archibald, a Canadian woman who worked at a homeless shelter before moving to Europe to be with her fiancé.
In a statement, her grieving family said that "she would have had no understanding of the callous cruelty that caused her death."
"She had room in her heart for everyone and believed strongly that every person was to be valued and respected."
The family urged people to donate to a homeless shelter or volunteer their time to their local communities.
"Tell them Chrissy sent you," they said.
Canadian Prime Minister Justin Trudeau said in a statement that he was "heartbroken" about the news.
"We grieve with the families and friends of those who have lost loved ones, and wish all those injured a speedy and full recovery," he said.
None of the other six fatalities have been publicly named.
Two French people injured
Four French people were injured in the London attack, which left seven dead and nearly 50 wounded, the French foreign minister said on Sunday.
"Four French people were injured and it seems one person was particularly affected," Foreign Minister Jean-Yves Le Drian told France Info radio.
French President Emmanuel Macron said French authorities would work to help the French victims and increase security for French voters in London "to show the force of democracy in the face of enemies of freedom."
French people were also among those injured in the attack on Westminster Bridge in March.
France is still under a state of emergency after a string of Islamic extremist attacks.
London Bridge victims receive emergency CPR
Metropolitan Police Assistant Commissioner Mark Rowley said an investigation has been launched into the attack, and has called for calm.
"At this stage, we believe that six people have died in addition to the three attackers shot dead by police," he said.
“I’d like to repeat our request for Londoners to avouid the London Bridge and Borough Market area.
“Our current belief is that there were three attackers. But the investigation is in an early stage and we still have some more inquiries to do.”
Prime Minister Theresa May's Conservative Party suspended national campaigning on Sunday for the upcoming June 8 UK election, a spokesman for May said.
"The Conservative Party will not be campaigning nationally today. We will review as the day goes on and as more details of the attack emerge," the spokesman said.
Earlier Ms May said the incident was a suspected terror attack.
“Following updates from police and security officials, I can confirm that the terrible incident in London is being treated as a potential act of terrorism," Ms May said.
“This is a fast moving investigation. I want to express my huge gratitude to the police and emergency services who are on the scene. Our thoughts are with those who are caught up in these dreadful events.”
She is expected to chair a meeting of the government's emergency response committee on Sunday local time.
London Mayor Sadiq Khan said he did not advocate postponing the imminent election.
People running from the scene at London Bridge
The attack occurred with the UK still reeling from a bombing in the northern town of Manchester last week in which 22 people were killed.
They also came just days before Britain goes to the polls for a general election on Thursday.
Witnesses on London Bridge reported seeing a van mounting the pavement and hitting pedestrians and a man running with a knife.
"There was a van that crashed into the fences on London Bridge. And then there was a man with a knife, he was running," said Dee, 26, who was visibly in shock and declined to give her last name.
"He came down the stairs and went to the bar."
erard Kavanar, 46, said he had seen a chef with "blood on his shoulder" in the area.
The London Ambulance Service said "multiple resources" were being sent to the scene.
The police were urging the public to run to a place of safety, or hide if they cannot.
AFP reporters saw two police helicopters over the area and several roads were shut down.
'Wounded people'
Will Heaven, managing editor of The Spectator magazine, said on Twitter that he saw "two casualties - one on pavement, one edge of road" and reported seeing armed police on the bridge.
BBC reporter Holly Jones, who was there at the time of the incident, said she saw a van driven by a man travelling "at about 50 miles (80 kilometres) an hour".
She said about five people were being treated for injuries after the vehicle mounted the pavement and hit them.
"There's several police boats with torchlights searching the Thames at the moment," she told BBC radio.
She added that she saw a man, who had his shirt off and was in handcuffs, being arrested by police.
'Large blade'
Husband and wife Ben and Natalie told BBC Radio 5 Live they were outside Borough Market when they witnessed the incident there.
Ben said: "We saw people running away and then I saw a man in red with a large blade, at a guess 10 inches long, stabbing a man, about three times.
"It looked like the man had been trying to intervene, but there wasn't much he could do. He was being stabbed quite coldly and he slumped to the ground."
Ben said the man then walked towards the Southwark Tavern. He said they saw a metal chair being thrown towards the man.
"Then we heard three gunshots, definitely gunshots, and we ran."
