The police response to the rampage, which saw officers shoot dead the attackers within eight minutes of police receiving the first call, has been widely praised.
"This has been a truly ghastly few weeks", said London police chief Dick, who said the spell of recent attacks was unprecedented in her working experience which began in 1983.
Trump said he had spoken with British Prime Minister Theresa May to express America's "unwavering support" and offer US assistance as the British government works to protect its citizens and bring the guilty to justice. News footage showed people fleeing the scene of Saturday's vehicle and knife attack, where 7 were killed and dozens injured, but one man stood out, walking slowly and appearing to try to prevent his pint of beer from spilling.
Scotland Yard said "increased physical measures" will be be in place in order to keep the public safe on London's bridges. A third attacker has not been identified. At least 12 people were arrested Sunday, including five men and seven women ranging in age from 19 to 60.
London Mayor Sadiq Khan said the city's "anger and grief" was indescribable.
In an early morning raid in east London, British counter-terrorism police detained more people today.
Ikenna Chigbo, in an interview with Britain's Independent Television News, described another of the arrested men as a nice guy who regularly invited neighbors to barbecues and played football and table tennis with them. He used to ask neighbours whether they prayed or not etc. "He was standing over there, I could see them from my window", Gasperri said.
"Yesterday - I'm actually in the process of moving home at the moment - I hired a van moving some bits".
Metropolitan Police Commissioner Cressida Dick said she wouldn't release further details in what she described as a fast-moving investigation.
With the attack dominating attention, a reduction in the number of police officers in England and Wales by nearly 20,000 during May's six years as interior minister from 2010 to 2016 shot to the top of the election agenda. Security had already become a key election issue following the Manchester bombing last month, in which 22 people were killed as they left an Ariana Grande concert.
She defended the country's policing resources Monday, saying that her Conservative government had protected police budgets.
UK PM says London mayor doing a good job following Saturday's attack; 'wrong to say anything else'.
The political tempo picked up again Monday with May saying opposition Labour Party leader Jeremy Corbyn is unfit to handle security and Brexit.
But as a former Interior Minister, May's record on security is also under scrutiny - police numbers were reduced every year under her watch and as Home Secretary she oversaw the domestic intelligence agency, MI5.