MARTIN: So what do we know right now?
"The safety and security of New Yorkers is our top priority, and we will continue to remain vigilant", said Cuomo.
The Justice Department filed a petition Thursday asking the Supreme Court to reinstate the ban, which would limit travel from six Muslim-majority countries.
The singer, whose concert at the MEN Arena in Manchester was the site of a suicide bomber just over a week ago, took to Twitter to post a heartfelt message following the atrocities that have taken place at London Bridge and Borough Market.
Police said in a tweet that "the incidents at #LondonBridge & #BoroughMarket were declared as terrorist incidents" and appeared to be connected. And police say that there have been stabbing incidents there and that they've sent in armed officers to address that.
She said the van came from the direction of central London and headed towards the south side of the river.
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Eyewitnesses reported panic as the incidents unfolded in the vicinity of a major transport hub and in an area packed with restaurants and bars.
Trump went on to promise support to London during the incident. "Thank you to the emergency services", Corbyn wrote on Twitter.More news: London Bridge: Van mows down pedestrians; stabbings at nearby cafe, witnesses say
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She said the investigation was fast moving and expressed gratitude to the police and emergency services who were at the scene.
Police said shots were fired and urged people to flee the area. A spokesman for Vice President Mike Pence said he also has been briefed and spoke with Trump from Air Force Two.
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.
"There's several police boats with torchlights searching the Thames at the moment", she told BBC radio. "Canada will always stand by the people of London".
There were also reports of a third incident, a stabbing in the Vauxhall area of London. He said he did not know how serious the injuries were. A Reuters reporter near the scene said she saw 10 police cars rushing towards London Bridge.
When he finally left the building he had been in he said all he could see was "lots of first aid kits and medical kinds of things and lots of armed police". And people just tried to get out of the way of the van. A police officer was stabbed outside Parliament.
Witnesses have reported seeing injured people on the ground on the bridge. Police have closed a nearby railway station and told people to get away from the area.
Terrorists attacked two popular tourist attractions in London late Saturday night, British police said, the third time in under three months England has suffered a terrorist attack.
Witnesses said they saw a white van struck pedestrians on London Bridge. Metropolitan police confirmed an incident but released few details.
Tony Murphy, who lives near the area, told Sky News he heard the sound of gunfire. Police are asking people to clear the area, and if they can not, to lock themselves in a room and shelter in place.
Home Secretary Amber Rudd said the attacks were "horrific" and "targeted at people enjoying their evening with friends and family".