"I don't think it's helpful for anyone to speculate on what is an ongoing investigation," May told ABC News chief anchor George Stephanopoulos in an interview that will air on "This Week" Sunday.
"The police and the security services are doing the work necessary to discover the full circumstances of this cowardly attack that's taken place, and to identify all those who are responsible," she said.
Trump's tweets took an apparent dig at British police, implying that they could have done more to stop the attack, which left at least 29 people injured.
"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!" he wrote in his first tweet.
Trump followed minutes later with more tweets that talked about the fight against terrorismand his administration's efforts to do so.
"Loser terrorists must be dealt with in a much tougher manner. The internet is their main recruitment tool which we must cut off & use better!" he wrote in another tweet six minutes later.
"The travel ban into the United States should be far larger, tougher and more specific-but stupidly, that would not be politically correct!" he wrote.
He went on, "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!"
Trump, addressing reporters briefly on camera, called the attack "an absolutely terrible thing."
"I'm going to call the prime minister right now," Trump said. "We have to be tougher and we have to be smarter."
Stephanopoulos asked May if a travel ban is something she would reconsider in light of Friday’s terror attack.
“I think what is important is that we're able to have the powers to look into people, to identify people who may be wanting to cause us harm and are plotting to cause us harm. And to be able to take the necessary action when people do cause us harm,” she said.