Trump also tweeted a pledge of help and support for London. We are in contact with and stand ready to assist our friends and allies in the United Kingdom as they respond, investigate, and recover. Gunfire erupted at the bridge, though witnesses said it could have come from police.
People at the scene on London Bridge have claimed the incident is a "terrorist attack".
Several people were reported killed and injured.
The attacks came within weeks of the May 22 suicide bombing in Manchester in northern England that killed 22 people at a pop concert by USA singer Ariana Grande. In March, four people were killed in London after Khalid Masood rammed his auto into pedestrians on Westminster Bridge before fatally stabbing a policeman outside the Houses of Parliament. She said she saw at least four or five people on the ground.
London Bridge and nearby Borough Market in London are in lockdown after two separate terror attacks. He later phoned May and offered condolences for the "brutal terror attacks", according to a White House statement.
Witnesses at the scene told the BBC that a white van ran into pedestrians on the bridge.
At 12.25am, both incidents were declared terrorist attacks.
An emergency response helicopter lands on London Bridge on June 3.
Assistant Commissioner Mark Rowley said in a statement on Twitter, "At this stage, we believe that six people have died in addition to the three attackers shot dead by police".
London Transport said the London Bridge tube station had closed at the request of police and was unlikely to reopen at least until end of service for the day.
The force said it was also attending a reported incident in Vauxhall.
The Metropolitan Police said they were called just after 10 p.m. (2100 GMT) to reports of a vehicle hitting pedestrians on the bridge, which crosses the River Thames in central London.
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British Prime Minister Theresa May has called the London Bridge incident a "potential act of terrorism".
Witness Elsbeth Smedley told CNN that a man ran into Elliot restaurant in Borough Market, and stabbed two people before running out.
The incident bore similarities to a March attack on Westminster Bridge, west of London Bridge, in which a man killed five people after driving into a crowd of pedestrians before stabbing a police officer in the grounds of parliament. Her office says she is being updated.
Ms Jones later reported seeing a man being arrested by police.
London authorities were investigating reports that a vehicle had hit pedestrians on London Bridge. Police confirmed that shots had been fired.
"A white van driver came speeding - probably about 50 miles per hour - veered off the road into the crowds of people who were walking along the pavement", she told BBC News. But these last two to three months, we had two confirmed terrorist attacks, 22 people dying up in Manchester at the concert.
He told Sky News that there were "about 20 of us" adding: "People were looking on their phones, people checked twitter and rang relatives who checked on news websites".
Jamie, a witness who was in a restaurant on Rochester Walk near London Bridge, told the Press Association: "We were in the Black and Blue restaurant, we heard a fight and everyone got up and everyone rushed out of the restaurant and we heard a massive, massive bang".
"It looked like he was aiming for groups of people".
U.S. President Donald Trump's spokesman says Trump has been briefed by his national security team and he will be provided with updates.
On March 22, a British-born terrorist drove his vehicle onto the pedestrian walkway at Westminster Bridge, killing four people and injuring 50. "People running - I've never ran so fast in my life", Joe Dillon, an American grad student at Kings College, told MSNBC.
A charity concert for victims of the Manchester attack, featuring Grande and other stars, is due to be held in the northwest English city on Sunday.