In the explosion, 22 people were injured.
Trump's tough talk came a day after he drew conservative criticism for pursuing an agreement with Democrats on young immigrants who had been living in the country illegally that would delay funding for his long-promised border wall.
His assertion that the London attackers "were in the sights of Scotland Yard" was either the revelation of shared intelligence or what the Prime Minister called unhelpful speculation.
"True or not - and I'm sure he doesn't know - this is so unhelpful from leader of our ally and intelligence partner", Timothy wrote on Twitter.
Britain's senior counterterrorism officer Mark Rowley told a news conference the explosion was caused by a suspected improvised explosive device (IED).
Security services told the Independent: "We don't even know who the suspects are so it's a bit hard to say".
However, Sadiq Khan refused to be drawn into the debate, saying he was "absolutely not going to go there".
- Donald J. Trump (@realDonaldTrump)Do you notice we are not having a gun debate right now? "The priority today is catching the individual or individuals responsible".
"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 continued.
The President did share highly classified intelligence about suspected IS plans, until then closely guarded among United States allies, with the Russian foreign minister during a meeting at the White House. "We are also aware of the attack in Burgundy, and our thoughts are with those wounded in that incident", Sanders said.
The president also addressed domestic and worldwide security, tweeting about his controversial travel ban and the ongoing fight against the Islamic State.
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