"Loser terrorists must be dealt with in a much tougher manner".
On Friday morning, Trump indicated that he expected harsher penalties for terrorists.
"We need to be smart, vigilant and tough".
When asked about Trump's comments, May said, "I never think it's helpful for anybody to speculate on what is an ongoing investigation".
The president weighed in as police in and around London carried out a manhunt for the person or persons who set off a crude incendiary bomb on a subway vehicle during Friday's morning rush hour.
Police say 30 people, including a young boy, were injured during the attack on a rush-hour train packed with school children and commuters.
Following the attack, Britain has raised threat level from severe to critical.
"I'm going to call the prime minister right now", Trump said.
He also asserted that he had made more progress in the war against the Islamic State (ISIS) than former President Barack Obama.
"Must be proactive & nasty!"
President Donald Trump is calling the explosion in London a "terrible thing".
And the White House said Mr Trump had pledged close collaboration with the United Kingdom "to stop attacks worldwide targeting innocent civilians and to combat extremism".
One of America's oldest and truest allies would appreciate it if Donald Trump would keep his opinions to himself. "The internet is their main recruitment tool which we must cut off & use better!" he added, without elaborating.
Trump was quick to criticise law enforcement in the wake of the attack and implied the assailants had been know to Scotland Yard.
The ban affects travelers from six mostly Muslim nations and refugees anywhere in the world. 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.