(ABC NEWS) -- Authorities have made "significant progress" in identifying the three suspects allegedly responsible for a terror attack in London Saturday night that killed seven people and injured dozens more, police said.

Several agencies are "working relentlessly" to "piece together exactly what occurred" and learn more about the attackers, Metropolitan Assistant Commissioner Mark Rowley said Sunday.

"Work is ongoing to understand more about them, their connections and whether they were assisted or supported by anyone else," Rowley said.

A series of arrests have been made in the attacks, police said. As of Sunday morning, 12 people in Barking, east London, were arrested in connection with the attacks, and police continued to search a number of addresses in the Barking area.

Just before 10 p.m. Saturday, white Renault van, which was recently hired by one of the attackers, plowed into a crowd of people on London Bridge.

American tourist Dan Nguyen told the BBC he was on London Bridge with his girlfriend when he "saw blinding white headlights weaving through cars and coming at us."

"It hit directly to the right of me. I saw a woman's body curled up in an unimaginable position," he told the BBC. "I looked ahead and saw there was a distance to go before the end of the bridge, so I braced myself to jump off the bridge into the river. Then I saw my girlfriend limping and sobbing so I ran back towards the scene to drag her away."

The van then continued on to Borough Market. There, three men -- who officials said were wearing fake suicide belts -- exited the vehicle and stabbed a number of people, police said.

The attackers were shot and killed by authorities just eight minutes after police were notified to the incident, said London Metropolitan Police's Cressida Dick. Eight police officers discharged their weapons, firing a total of 50 rounds, Rowley said. One bystander was hit by the gunfire, he said, but the injuries were not believed to be critical.

Seven victims were killed in the attack and another 48 victims were taken to hospitals, officials said. On Sunday, 36 victims remained hospitalized, 21 of them in critical condition, Rowley said.

Among the injured were a British Transport Police officer and an off-duty Metropolitan Police officer, authorities said. The British Transport Officer who was injured was among the first on the scene and was "able to recount how he faced the attackers with only his baton" despite being "seriously unwell," said Chief Constable Paul Crowther.

British Prime Minister Theresa May referred to the events as a "brutal terrorist attack" and said "there is far too much tolerance for extremism in our country."

Britain has been plagued with three terror attacks since March. May said that while the attacks are not connected, "they are bound together by the single evil ideology that is Islamic extremism."

"Defeating this ideology is one of the great challenges of our times," she said, adding that the internet is a breeding ground for extremism.

"This was a deliberate and cowardly attack on innocent Londoners and visitors to our city enjoying their Saturday night," Khan said. "I condemn it in the strongest possible terms. There is no justification whatsoever for such barbaric acts."

A moment of silence will be held Tuesday at 11 a.m. local time "in remembrance of those who lost their lives and all others affected by the attacks in London Saturday night," according to an announcement from Downing Street. Flags will remain at half-mast on Whitehall government buildings until Tuesday evening.

Britain's general election will take place Thursday as planned, May said.

"Violence can never be allowed to disrupt the democratic process," May said. "So those campaigns will resume in full tomorrow, and the general election will go ahead as planned, on Thursday."

ABC News' David Caplan, Matt Foster, Tara Fowler, Joshua Hoyos, Kirit Radia, Brendan Rand, Emily Shapiro, Dean Schabner and Devin Villacis contributed to this report.