Trump on Friday also used the London train attack to renew calls for his controversial travel ban on travelers from several predominantly Muslim countries, which is the subject of fierce legal battles in the U.S. but has partially gone into effect.
More than 20 people were injured when the improvised explosive device ignited on a District Line train at Parsons Green in the height of morning rush hour.
Trump then uses the bombing to sell his beleaguered travel ban, which is enduring various legal challenges but now prevents most refugees from entering the US.
"As I said, the police and security services have been working to discover the full circumstances of this cowardly attack and to identify all those responsible", May commented on Trump's tweet.
He did not immediately offer condolences to the British people.
"Meaning, he was saying generally, terrorists are a focus for Scotland Yard?".
Meanwhile, the United States president on Friday claimed his administration had "made more progress in the last nine months" against the Daesh (ISIL) terrorist group than his predecessor, Barack Obama.
Trump said he had been briefed on the London attack, and said he had been told about "new risks of things happening".
After the terrorist attack in Manchester in May which killed 23 people, Trump said: "I won't call them monsters because they would like that term".
Trump also took the opportunity to push his proposed travel ban against several Muslim-majority nations, which has been tied up in court. Police said they were investigating it as a terrorist attack.
After the Manchester Arena attack, intelligence from the United Kingdom investigation - including the name of the attacker and photos of his device - was leaked by USA government sources to the American media. The US president has in the past been accused of reacting to suspected terrorist incidents before the facts are fully known.
At least 29 people were injured in the attack after a device in an Lidl bag was trigged by a timer and partially exploded. Photos showing crime scene evidence appeared in US media; the bombing suspect's name was revealed while British officials were still withholding it. Trump said May was "very angry" over the leaks.