The agency additionally tweeted a third incident has been reported in the Vauxhall neighborhood of South London, some 20 minutes away by auto.
Will Heaven, the managing editor of The Spectator magazine, said on Twitter he saw "two casualties - one on pavement, one edge of road" and reported seeing armed police on the bridge.
Two and a half hours after the initial attack, British police officially declared the incidents on London Bridge and at Borough Market were terror incidents.
Shortly after that, officers said there had been reports of stabbings at Borough Market.
London Mayor Sadiq Khan has condemned the incidents at London Bridge and on Borough Market, describing them as "a deliberate and cowardly attack on innocent Londoners". It was later determined that the Vauxhall incident was a stabbing that was not connected to the other two.
Whatever the United States can do to help out in London and the U.
Transport for London says busy London Bridge station has been closed at the request of police.
There have also been unconfirmed reports from witnesses to Reuters, BBC News, CNN and The Telegraph of stabbings. They also issued safety instructions to those in the areas of the incidents, warning people to run, hide, and contact police when it is safe to do so.
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"They looked like just a toy to me".
British prime minister Theresa May is being briefed on the incidents, along with US President Donald Trump.
Witnesses said they saw a white van struck pedestrians on London Bridge.
There were also reports that shots were fired with multiple people "seriously injured".
London Bridge has been shut down during what became a scene of panic and chaos that began as just another mild weekend night was unfolding at the tourist hotspot.
"I asked what was going on an a police officer said a van started running over people".
A witness, Mark Roberts, told CNN that he was on the bridge when a van came swerving down the roadway at a high rate of speed.
"The police were absolutely brilliant, they came in and explained the situation", he said".
One terrified woman said she was at a restaurant and police swarmed on the area. The van reportedly hit several people, and the witness said he then saw several bodies on the ground that were not moving. Police officers yelled at people to run from the area.
After ramming the auto into a barrier outside the Houses of Parliament, the driver, 52-year-old Khalid Masood, got out and stabbed a police officer to death before being gunned down by responding officers.