Trump also used the incident to defend his travel ban targeting six mostly Muslim nations.
"True or not - and I'm sure he doesn't know - this is so unhelpful from leader of our ally and intelligence partner", tweeted Timothy, who was May's chief of staff until the June general election and worked for her as a senior adviser when she was home secretary.
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.
He did not immediately offer condolences to the British people.
In a White House statement, hours after his morning tweets, the president "pledged to continue close collaboration with the United Kingdom to stop attacks worldwide targeting innocent civilians and to combat extremism". "Scotland Yard has been a leader, as our Federal Bureau of Investigation has been a leader".
"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!" he tweeted.
"I think what the President was communicating is that, obviously, all of our law enforcement efforts are focused on this terrorist threat, for years", McMaster said.
The ambulance service says none of the injuries is thought to be serious or life-threatening.
On that occasion, May was forced to upbraid the U.S. leader, saying "I think Donald Trump is wrong in what he said about Sadiq Khan" after the London Bridge attack. Somebody will say, 'Oh freedom of speech, freedom of speech.' These are foolish people. Police are treating an explosion in an underground train carriage as a "terrorist incident". Police said they were investigating it as a terrorist attack.
Stephanopoulos asked May if a travel ban is something she would reconsider in light of Friday's terror attack.
"We have to be tougher and we have to be smarter", Trump told reporters before going into the Oval Office. "We need the Travel Ban as an extra level of safety!" he tweeted.
On Monday, Trump's administration scored a key legal victory related to his travel ban when the Supreme Court granted a temporary stay of the ban's effect on a group of around 24,000 refugees.