The Drudge tweet said there were "fears of new terror attack after van "mows down 20 people" on London Bridge", but the perpetrators, motive, and number of casualties involved in the incident were still unknown.
Assistant Commissioner Mark Rowley of the Metropolitan Police said: "At this stage, we believe that six people have died in addition to the three attackers shot dead by police".
The attack in central London came just weeks after a suicide bombing at a concert in Manchester left 22 dead, and it recalled an attack in March when a man drove a vehicle into pedestrians near the seat of Parliament, killing five.
The attack had harrowing echoes of the one on London's Westminster Bridge in March, when British Muslim convert Khalid Masood rammed his auto into pedestrians before crashing into the barriers surrounding parliament. A further 12 were arrested after raids at a block of flats in east London. He turned and saw three men wearing belts or vests with packets around the belly. They include a concert by US pop star Ariana Grande - who was performing at the venue targeted by terrorists last month - to raise money for people affected by that attack. "The Uber stopped, we asked people what was going on - people said there was shooting", said Yoann Belmere, 40, a French banker living in London. Former vice president and 2000 Democratic presidential nominee Al Gore said on CNN's "State of the Union: "I don't think that a major terrorist attack like this is the time to be divisive and to criticize a mayor who's trying to organize his city's response to this attack".
"Severe means an attack across the country is still highly likely", he said, warning citizens to be vigilant.
"It is time to say 'Enough is enough, '" May said.
May said the attacks weren't directly connected, but that "terrorism breeds terrorism" and attackers copy one another.More news: Philippine casino attacker a gambling addict, not terrorist
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Actor-comedian Chris Addison encouraged people to tweet ways in which they were reeling.
Witnesses reported seeing injured people on the ground on the bridge.
The mayor in question is London's Sadiq Khan, who responded to the president through a spokesperson.
Holly Jones, a BBC reporter who was on the bridge as the attack took place, said the van drove at high speed, veering into pedestrians.
Describing the scene outside of Applebee's, the establishment in which she took refuge, Ms Owen said: "It was horrible, horrible".
People from around the world were caught up as hundreds cowered in pubs and restaurants, barricading themselves inside as the attackers stalked the streets. Police officers yelled at people to run from the area, and blasts were heard as officers performed a series of controlled explosions.
A British Transport Police officer with less than two years on the force - and armed only with a baton - was in stable condition after suffering injuries, police confirmed in a statement Sunday. They had already attacked and killed members of the public and needed to be stopped immediately.
State department called the assaults "cowardly attacks targeting innocent civilians" and added: "The United States stands ready to provide any assistance authorities in the United Kingdom may request". "So let me look into it".