British police responded to multiple security incidents across London on Saturday as a van plowed into pedestrians on London Bridge and at least one assailant went on a stabbing rampage in an area of the capital known for its pubs and lively nightlife.

Metropolitan Police said the incidents were terrorism and appeared to be connected. It was not entirely clear if the police operation was over.

Earlier, Prime Minister Theresa May said the attacks were being investigated as a "potential act of terrorism."

The first incident took place on London Bridge, where witnesses described seeing a white van mounting the sidewalk and killing 7 people at about 10:30 p.m. A BBC reporter who was on the bridge at the time said the van was being driven at around 50 mph by a male suspect.

London Bridge, which crosses the River Thames in London, was closed in both directions.

In the incident at Borough Market, a nearby area that houses many food stalls and pubs and is popular with tourists, Metropolitan police said armed officers had been sent to the area after reports of stabbings at a restaurant.

Police said shots were fired and urged people to flee the area. However, it was not clear if the shots were fired by police or an assailant or assailants.

There were also reports of a third incident, a stabbing in the Vauxhall area of London. That was subsequently said to be unrelated to the terror attack.

Some witnesses reported seeing as many as three attackers, a figure not confirmed by police.

Police urged Londoners to be calm and vigilant and circulated a message that read: "Run," "Hide," "Tell."

The British Prime Minister's office said May was being regularly updated on the situation, and the White House said President Trump has been briefed.

"Whatever the United States can do to help out in London and the U. K., we will be there - WE ARE WITH YOU. GOD BLESS!" Trump tweeted.

Reports of the incident reflected fear that the incident could be terrorism. Britain has weathered two terrorism attacks in recent months. In March, four people were killed in London after Khalid Masood rammed his car into pedestrians on Westminster Bridge before fatally stabbing a policeman outside the Houses of Parliament.

On May 22, a British-born suicide bomber killed 22 people and injured 59 others at an Ariana Grande concert in Manchester, England.

The attack came on the eve of a benefit concert Grande is scheduled to play in Manchester on Sunday in aid of the victims and their families.