He also suggested that the perpetrator was known to authorities and recruited on the Internet, prompting British Prime Minister Theresa May and a London police spokesperson to publicly rebuke the President.
"Another attack in London by a loser terrorist. These are sick and demented people who were in the sights of Scotland Yard. Must be proactive!" he tweeted.
"Loser terrorists must be dealt with in a much tougher manner.The internet is their main recruitment tool which we must cut off & use better!" he continued.
Trump then added, "The travel ban into the United States should be far larger, tougher and more specific-but stupidly, that would not be politically correct!"
Trump similarly referred to his travel ban
back in June immediately after news reports surfaced about the London Bridge terror attacks.
In a fourth tweet Friday morning, Trump said, "We have made more progress in the last nine months against ISIS than the Obama Administration has made in 8 years.Must be proactive & nasty!"
Speaking to members of the US Air Force at Joint Base Andrews outside Washington, D.C., Friday afternoon, Trump said: "Radical Islamic terrorism, it will be eradicated."
The President added that he had called May about the attack.
"I spoke with a wonderful woman, British Prime Minster Theresa May, this morning and relayed America's deepest sympathy as well as our absolute commitment to eradicate the terrorists from our planet," Trump said.
The President added: "America and our allies will never be intimidated. We will defend our people, our nations and our civilization from all who dare to threaten our way of life."
Police say an "improvised explosive device" was detonated
on a train in west London Friday, injuring at least 18 people, in an incident authorities are treating as terrorism. Authorities in London are still investigating the attack, and it's not immediately clear who was responsible or what Trump was referring to in suggesting that the perpetrators were known to authorities.
Asked about Trump's assertion that the attack was perpetrated by people known to authorities, May said it is "never helpful for anyone to speculate on what is an ongoing investigation."
And a police spokesperson told CNN that Trump's comment is "pure speculation given we don't know who involved. Any speculation is unhelpful."
London Mayor Sadiq Khan said he was coordinating with the police and authorities and urged Londoners to "remain calm and vigilant."
White House national security adviser H.R. McMaster attempted to explain the President's morning assertion that culprits behind the explosion were known to British law enforcement, but offered little clarity.
McMaster didn't answer directly at a White House briefing whether Trump was revealing an intelligence assessment or whether he was just speculating.
"What the President was communicating is that obviously all of our law enforcement efforts are focused on this terrorism threat for years," McMaster said. "Scotland Yard has been a leader, and our FBI has been a leader. So I think if there was a terrorist attack here, God forbid, that we would say that they were in the sights of the FBI. So I think he didn't mean anything beyond that."
Pressed to explain further, McMaster said that US and UK agencies are both working to prevent terrorism.
"I think he means generally that this kind of activity is what we're trying to prevent," McMaster said. "So these organizations that are responsible for whatever comes out of this investigation remains to be seen. It is likely that law enforcement had been working on that problem set."
Trump called for travel ban after June attacks
This isn't the first time Trump has used terrorist attacks in London to call for his travel ban. After two terror attacks in the city in June, Trump seized on the moment.
"We need to be smart, vigilant and tough. We need the courts to give us back our rights. We need the Travel Ban as an extra level of safety!" he tweeted.
Khan and Trump publicly feuded following the June attacks after the US President misconstrued a statement from Khan saying there was "no cause for alarm" due to the visible police activity following the incident.
Trump responded on Twitter: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'"
The Supreme Court granted
Tuesday a Trump administration request to continue to bar most refugees under its travel ban.
The travel ban bars certain people from Iran, Libya, Somalia, Sudan, Syria and Yemen from entering the US.
The issue concerning the scope of the travel ban has been making its way through the courts since last spring, when the Supreme Court allowed Trump's ban to go into effect except for those with a "bona fide" relationship to the United States. The order might give hope to supporters of the ban, but it may also simply reflect a desire on the part of the justices to maintain the status quo until the justices can hear the case next month.
The ban was ordered to be in effect for 90 days, during which the administration would assess vetting procedures and whether they're secure enough. Trump's executive order also requires reports on its effectiveness.
That clock is set to run out before the end of this month
, and the administration has not indicated yet what it will do next.