By Steve Almasy and Natalie Gallon

PHILADELPHIA (CNN/CBS/AP) — Three attackers killed several people in two terror incidents in London on Saturday night.

Six people were killed during Saturday night’s terror attacks at London Bridge and a nearby market, Mark Rowley of the Metropolitan Police said. Police killed the three attackers.

More than 30 people were taken to five hospitals after the terror attacks Saturday night, London Ambulance Service Assistant Director of Operations Peter Rhodes says. Other people were treated at the scene, Rhodes says.

More than 80 medics responded to the scenes at London Bridge and Borough Market.

At 0025hrs 4/6/17 the incidents at #LondonBridge & #BoroughMarket were declared as terrorist incidents. — Metropolitan Police (@metpoliceuk) June 3, 2017

A van plowed into pedestrians on London Bridge and two people were stabbed at a nearby cafe.

A witness on the bridge told CNN the van mowed down pedestrians as it sped south across the bridge, leaving bodies lying in the roadway.

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Another witness, who was in the cafe, said a man with a “massive knife” entered the restaurant at Borough Market, just south of the bridge, and stabbed two people inside. The patrons sheltered in the basement and police then arrived at the scene, the witness said. The condition of the stabbed people was not known.

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The BBC reports more than one person died on London Bridge. Nick Brandon of British Transport Police told The Associated Press that they received reports of “multiple” casualties in an incident possibly involving a knife and a vehicle.

A witness of the London Bridge incident said the attackers were yelling, “This is for Allah.”

Police tell The Associated Press that shots have been fired at Borough Market after responding to reports of stabbings.

London Bridge Tube station was closed and London Bridge was closed in both directions.

British Prime Minister Theresa May says the “terrible incident in London is being treated as a potential act of terrorism,” according to a statement.

The prime minister will chair a meeting of the Government’s Cobra emergency committee — her top security advisers — Sunday, according to a statement from 10 Downing Street, via Britain’s Press Association.

London Mayor Sadiq Khan called it a “horrific terrorist attack.”

“We don’t yet know the full details, but this was a deliberate and cowardly attack on innocent Londoners and visitors to our city enjoying their Saturday night. I condemn it in the strongest possible terms. There is no justification whatsoever for such barbaric acts,” Khan said.

My statement on the cowardly terrorist attack in London tonight: https://t.co/7GYYdImIU8

Please continue to follow @metpoliceuk for updates pic.twitter.com/xxTbH2o2JN — Sadiq Khan (@SadiqKhan) June 4, 2017

There were reports of a third incident in the Vauxhall area, but police say it’s not related to the other two.

Mark Roberts, the witness on the bridge, said the van was traveling south across the River Thames at a high rate of speed and was swerving as it struck several people, knocking one person “about 20 feet into the air.”

The van swerved into oncoming lanes before hitting a bus stop and coming to a stop, Roberts said.

“Within my line of sight, there were five or six people on the ground that were not moving,” he said. “It looked to me that the van was aiming at the people.”

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Roberts said he heard what sounded like gunshots about 10 minutes later. He estimated 100 people were on the bridge at the time, fewer than earlier in the night because it was getting late.

“I froze, to be honest,” Roberts said. “As I was thinking … which direction should I run, the van swerved across the other side of the bridge from me.”

Borough Market, where the stabbing occurred, is a popular food market in south London, just south of London Bridge, with gourmet food and produce stalls and several restaurants inside.

A witness said they were in the front of Elliot’s Cafe when a large group of people started running up the street from Borough Market.

“Someone said, ‘What is going on?’ and one of the people running said, ‘There is a man with a knife up there and he is coming this way.’ There was complete panic as everyone ran to the back of the restaurant and crouched down trying to hide themselves from view,” the witness said.

“A man suddenly appeared in the restaurant with a massive knife — some people in the restaurant believe there may have been another man — but it was so chaotic it was hard to tell,” the witness said.

The man with the knife stabbed a waitress, who was hiding behind a partition, in the neck and stabbed a man in the back before running out of the restaurant.

Police activity spread throughout the Borough Market area. Officers rushed into Katzenjammers bar and ordered people to sit on the floor, patron Paul Connell told CNN.

“The police were absolutely brilliant, they came in and explained the situation,” he said. ” Armed police came in. They told us to remain on the floor but to stay calm. We were eventually led out of the bar and some kind people working in a hotel let us come in to use the bathroom and to give us water.”

CBS News correspondent Elizabeth Palmer reports that security in the country “had been scaled back just last week” following the attack in Manchester.

"Security was heightened all over the country" after attack in Manchester, "but it had been scaled back just last week," @elizapalmer says pic.twitter.com/OVvJcLynXU — CBS News (@CBSNews) June 3, 2017

Video was posted on social media showing police entering a London bar and telling patrons to get down.

WATCH: Video posted on social media shows officers entering a London bar and telling people to "get down." https://t.co/YiEGXbVRQ2 pic.twitter.com/tH4BlETkJ4 — CBS News (@CBSNews) June 3, 2017

The U.S. national security team has briefed President Donald Trump on the situation and will continue to provide him with updates, White House Press Secretary Sean Spicer said.

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Trump took to Twitter following the reported incidents, saying that the U.S. needs the travel ban his administration tried to implement.

“We need to be smart, vigilant and tough. We need the courts to give us back our rights. We need the Travel Ban as an extra level of safety,” the president tweeted.

We need to be smart, vigilant and tough. We need the courts to give us back our rights. We need the Travel Ban as an extra level of safety! — Donald J. Trump (@realDonaldTrump) June 3, 2017

Trump also tweeted that the U.S. will be by the United Kingdom’s side following these attacks.

“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!” the president said.

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! — Donald J. Trump (@realDonaldTrump) June 3, 2017

The U.S. embassy in London tweeted: “Please avoid the area and monitor local news/@metpoliceuk for updates.”

England has been on edge since May 22, when a suicide bomber killed 22 people at an Ariana Grande concert at the Manchester Arena.

The bridge incident also comes more than two months after a man drove an SUV into a crowd on the sidewalk along Westminster Bridge in London, killing at least four people.

After ramming the car into a barrier outside the Houses of Parliament, the driver got out and stabbed a police officer to death. The attacker was gunned down by a police officer.

The assailant, Khalid Masood, 52, of West Midlands, reportedly had a criminal record and may have had connections to violent extremism, British Prime Minister Theresa May said.

(The-CNN-Wire ™ & © 2017 Cable News Network, Inc., a Time Warner Company. All rights reserved.)