At 6:42 a.m., Mr. Trump tweeted that “sick and demented people who were in the sights of Scotland Yard” carried out the attack, which injured at least 29 people in the blast and ensuing panic. It was not clear where Mr. Trump got that information, though 23 minutes earlier, “Fox & Friends,” a program he regularly watches, broadcast a report in which a security analyst said he feared that the London police had already known the identity of the attackers.
“Can someone tell Scotland Yard?” asked Brian Kilmeade, one of the hosts of the program.
White House officials tried to play down the contretemps, saying Mr. Trump was referring to the longstanding efforts of British law enforcement authorities to investigate would-be terrorists, not to anyone involved in Friday’s attack.
“What the president was communicating is that obviously all of our law enforcement efforts are focused on this terrorist threat for years,” said the national security adviser, Lt. Gen. H. R. McMaster. “Scotland Yard has been a leader, as our F.B.I. has been a leader.”
The press secretary, Sarah Huckabee Sanders, said she believed that Mr. Trump’s tweet had come up in the conversation with Mrs. May, though she did not characterize the exchange. Mr. Trump, for his part, referred to Mrs. May as “a wonderful woman.” But Mrs. May made her displeasure clear earlier in the day when she told reporters, “I never think it’s helpful for anybody to speculate on what is an ongoing investigation.”
Others were more scathing. Mrs. May’s former chief of staff, Nick Timothy, wrote on Twitter, “True or not — and I’m sure he doesn’t know — this is so unhelpful from leader of our ally and intelligence partner.”
The president has had a strained relationship with Britain since before he took office. Soon after he was elected, he suggested that Nigel Farage, a leader of Britain’s movement to leave the European Union, should be made the British ambassador to the United States — a decision that, London pointed out, was not Mr. Trump’s to make.
Mrs. May and Mr. Trump have had an awkward relationship, going back to their first meeting, when people criticized the way he gripped her hand. Last month, she joined other world leaders in criticizing his response to the white supremacist violence in Charlottesville, Va.
For Mr. Trump, the news of another terrorist attack also offered a moment to do some political repositioning by returning to themes that have animated him since the presidential campaign. After a week in which his pursuit of a compromise with Democrats on immigration rattled his supporters, the president appeared eager to seize on a range of red-meat issues to prove his bona fides.
In addition to the travel ban, Mr. Trump said that no agreement protecting undocumented immigrants brought to the United States as children could include “chain migration” — shorthand among immigration restrictionists for laws that enable immigrants to petition the government for papers for family members.
“Trump underestimated the reaction of throwing DACA out there for debate, and now he’s telling us he really wanted to use that to get all the things he could get on enforcement,” said Representative Steve King, Republican of Iowa and an immigration hard-liner. “I don’t think he realized the base was going to blow up on him.”
Mr. Trump even weighed in on the dispute over Jemele Hill, a black female commentator at ESPN, who tweeted that the president was a “white supremacist.” “ESPN is paying a really big price for its politics,” he tweeted. “Apologize for untruth!” Ms. Hill has apologized, but Ms. Sanders said her comment was a “fireable offense.”
Some polls have shown that the president’s political base would mostly support preserving Deferred Action for Childhood Arrivals, or DACA, which temporarily shields 800,000 young immigrants from deportation. But Mr. King said he was skeptical of those numbers.
Neil Newhouse, a Republican pollster who conducted one of the surveys, said Mr. Trump was engaging in an exercise that he believes has been effective in the past. “He has an ability to hold up a shiny object and his base follows it unerringly, and he’s really good at it,” Mr. Newhouse said.
Mr. Trump also does not hesitate to point fingers after suspicious explosions in European cities. Some counterterrorism experts were also asking whether Friday’s explosion was another instance in which the police overseas had mishandled tips about a possible attack. On “Fox & Friends” shortly before the president tweeted, Jim Hanson, a security analyst who served in the Army Special Forces, said, “My fear, again, is that we’re going to find out this is someone who is known to police.”
A website for the firm Mr. Hanson runs, Security Studies Group, says it focuses on “defending the value of American power against the true threats we face” against a Washington elite that has been “unable or unwilling to address and communicate the most basic requirements of American nationhood.”
Mr. Trump also took aim at the Islamic State, which claimed responsibility for the attack. He tweeted that his “proactive and nasty” military campaign against the jihadists had made more progress in eight months than the Obama administration had in eight years.
And Mr. Trump used characteristically pungent language about the assailants themselves. “Loser terrorists must be dealt with in a much tougher manner,” he tweeted.