Police initially said officers were also responding to a third incident, in the Vauxhall neighborhood, but later said that turned out to be an unrelated stabbing.
Two police boats are patrolling on the River Thames overnight, working to evacuate people as well as searching for possible victims who may have been knocked off or thrown off the bridge by the terrorists. They later clarified that it was a stabbing that was not connected to the other incidents.
The bridge is in lock down and the area around it is closed with bus routes being diverted, as armed police and a bomb squad attend the scene and boats search the water.
British Prime Minister Theresa May has been briefed on the incident and is in touch with officials, Downing Street said.
Trump expressed support for both the city of London and the broader United Kingdom while reiterating his call for a travel ban that has been consistently struck down by the USA court system. The London Bridge and Borough stations have been closed down.
"More police came over, I guess they were on radio or something because in around like two or five seconds they shot all the three men down".
A photographer has told of the moment he saw an attacker lying on the ground with what appeared to be canisters strapped to his chest after a terror rampage at London Bridge and Borough Market.
"A white van driver came speeding - probably about 50mph - veered of the road into the crowds of people who were walking along the pavement", she told BBC News. May has described the incidents as "potential acts of terrorism".
Facebook activated its safety check feature for the London area.
Police have also responded to an incident at Borough Market, which is within half a mile of the London Bridge, and Vauxhall, which is three miles away.
In March, a British convert to Islam ran down people with a vehicle on Westminster Bridge, killing four, then stabbed a policeman to death outside Parliament. I was in the back of an Uber cab driving south over London Bridge.
Hours after the attacks began, a large area of central London remained cordoned off and police told people to avoid the area, leaving tourists and revelers struggling to get home.
England has been under heightened alert since a bomb was detonated at an Ariana Grande concert in Manchester nearly two weeks ago, killing 22 and wounding more than 100 as they left the venue. Grande and others are slated to return to Manchester on Sunday for a benefit concert.