Another security official said British police were leading on the incident.British police said more than one person had been killed at London Bridge in first of multiple incidents in central London on Saturday night.
The BBC and Reuters report that police are seeking three male suspects.
"Armed officers responded and shots have been fired", Met Police said.
Armed police responded to a second incident at nearby Borough Market, and Metropolitan police said that a third incident was under investigation in the Vauxhall area, which later turned out to be unrelated.
The Metropolitan Police force said it had declared the attacks as "terrorist incidents".
"They were running out going, 'This is for Allah, ' and they stabbed this girl I don't know how many times", the man said.
President Donald Trump tweeted about the incident.
"Whatever the United States can do to help out in London and the U.K., we will be there", he tweeted.
London Bridge is closed in both directions and the London Bridge rail station has also been closed.
Several witnesses also reported hearing gunshots.
Two more arrests in Manchester attack investigation
Home Secretary Amber Rudd had earlier criticized United States officials for sharing details of the atrocity with American media. A vivid blue flash of the rucksack's inner lining matches crime scene pictures published by the New York Times .
In horrifying footage taken from the scene, police can be heard shouting "clear the area, now" while screaming people can be seen running in fear for their lives.
"I'd say there are about four severely injured people".
He told Sky News: "It was about 10.15pm I was in the back of an Uber cab driving over London Bridge.there was somebody down on the pavement with a small crowd around them clearly very concerned.
It slammed into several people - knocking one person about 20 feet into the air, he said.
Taxi driver Chris was on London Bridge as the incident unfolded.
"He swerved right 'round me and then hit about five or six people". He hit about two people in front of me and then three behind. One image taken by a witness showed a man on the ground surrounded by police; he appeared to be wearing a vest with canisters attached to it.
At nearby Borough Market there were reports of three men jumping out of a van with long knives who then began stabbing people.
Another witness, Mark Roberts, told CNN he saw the van hit multiple people before hitting a bus stop and stopping.
Indians are also speculated to be in the area as there is an India vs Pakistan match scheduled at the Edgbaston Cricket Stadium in Birmingham on June 4.
Ms Jones said police were on the scene within two minutes, quickly followed by ambulances.
On March 22, the British Parliament building was attacked by a man who ran over pedestrians with a auto and then stabbed several people.
Grande visited victims of the bombing in the hospital Saturday and is scheduled to perform at a star-studded benefit concert in Manchester on Sunday.