He also offered implied criticism of law enforcement, saying "these are sick and demented people who were in the sights of Scotland Yard". As the attack unfolded, Trump on Twitter advocated for his court-blocked "travel ban", calling it "an extra level of safety".
Asked about his tweet on the travel ban, Trump said "we have to be tougher and we have to be smarter".
Although he confirmed he had been briefed on London, the President did not say whether that briefing happened before or after his tweets.
His comments appeared to point the finger at British police.
Trump's tweets even sparked anger on the social network.
In a TV statement on Saturday, Prime Minister Theresa May raised the United Kingdom terror threat from "severe" to "critical", prompting fear another attack may be imminent.
Trump also claimed that his administration has accomplished more to defeat ISIS in nine months than Obama's Administration did in eight years.
"Must be proactive & nasty!"
The President added that he had called May about the attack. "The internet is their main recruitment tool which we must cut off & use better!" "We have to see Bill Gates and a lot of different people that really understand what's happening".
The bomber's identity and details of the probe leaked to U.S. media before British officials felt ready to disclose them.
"Another attack in London by a loser terrorist", he wrote.
Metropolitan Police Deputy Assistant Commissioner Neil Basu, the senior national coordinator for counterterrorism policing, said the blaze was being treated as a "terrorist incident" and investigators were examining the remains of an improvised explosive device.
The latest version of his travel ban, initially announced in a botched late-January rollout, calls for a ban on people entering the USA from a short list of terror-prone countries that are also Muslim-majority nations.
The New York Times scooped British authorities and other media by publishing photographs from the scene of remnants of the bomb.
Trump's tweet could amount to a security breach if it emerges that he was leaking sensitive information on Friday, and not indulging in pure speculation as London police have claimed.