Theresa May has raised concerns with Donald Trump over his claim the perpetrators of the Parsons Green Tube bombing had been "in the sights" of Scotland Yard.
After chairing a meeting of the government's Cobra emergencies committee, the prime minister publicly rebuked the US president, saying was not "helpful" to speculate on what was an ongoing investigation.
Mrs May is understood to have raised the issue during a "cordial" telephone call.
The president's intervention threatened to place fresh strain on the US-UK intelligence-sharing relationship which has come under pressure a number of times since he entered the White House.
In a trademark tweet issued within hours of the blast, Mr Trump wrote: "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!"
The Metropolitan Police said the US president's comments – which did not correspond with any information released by the UK authorities – were "unhelpful" and "pure speculation".
In Downing Street, Mrs May said: "I never think it's helpful for anybody to speculate on what is an ongoing investigation.
"The police and security services are working to discover the full circumstances of this cowardly attack and to identify all those responsible."
Asked later whether he had been briefed on any intelligence about the attack, Mr Trump appeared to sidestep the issue saying he had been briefed "on numerous things" including North Korea.
"It's a terrible thing. It just keeps going and going, and we have to be very smart, we have to be very, very tough. Perhaps we are not nearly tough enough," he said.
"It's just an absolutely terrible thing. In fact, I'm going to call the prime minister right now. We have to be tougher and we have to be smarter."
Downing Street said Mr Trump had offered his condolences over the attack during a telephone call.
A spokesman said: "President Trump called the prime minister earlier today to offer his condolences over this morning's cowardly attack in London.
The White House said: "President Donald J Trump spoke with prime minister Theresa May of the United Kingdom to convey his sympathies and prayers for those injured in the terrorist attack today in London.
"The President pledged to continue close collaboration with the United Kingdom to stop attacks worldwide targeting innocent civilians and to combat extremism."
"They also discussed North Korea's latest missile test, agreeing it was a reckless provocation and that China must now use all its leverage to bring pressure to bear on the North Korean regime to ensure they change course and end these illegal tests."
The latest spat comes after British police temporarily suspended intelligence-sharing with the US in the wake of the Manchester Arena bombing in May following a series of leaks to American media.
CBS disclosed the name of the bomber, Salman Abedi, citing US sources, at a time when the British authorities were asking media to withhold the information to protect the investigation.
The New York Times then published detailed photographs taken from the bomb scene which had been taken by British investigators.
The "special relationship" had already come under strain earlier in the year, when the then White House press secretary Sean Spicer repeated claims that GCHQ, the UK surveillance agency, had been involved in bugging the Trump campaign on behalf of Barack Obama.
His comments drew a rare public statement from GCHQ denouncing the allegation as "utterly ridiculous".
London Mayor Sadiq Khan, who clashed with Mr Trump over his response to the London Bridge terror attack, would not be drawn on the president's latest comments.
"I've simply been too busy this morning to look at my Twitter," he told LBC Radio.
"My priority is making sure that we do what we can to keep Londoners safe."
A City Hall source said: "He hopes people don't speculate on things before we know the full facts. That's quite clear what he thinks about that."
