The attacker's identity and details of the investigation were revealed in USA media before British authorities made the information public, while The New York Times published photographs from the scene, as well as images of the bomb.
Prime Minister Theresa May alluded to Trump's Twitter post in an interview with reporters, saying "I never think it's helpful for anybody to speculate on what is an ongoing investigation".
It is thought police have now identified the Parsons Green tube bomber using CCTV but Scotland Yard hasn't named the suspect or released an image, amid fears they could be armed and may have planted other explosive devices. "Any speculation is unhelpful".More news: Not Against Any Project But Bullet Train Economically Unviable: Congress
At an event at Joint Base Andrews in Maryland, Trump said he offered prayers for London and said "radical Islamic terrorism it will be eradicated, believe me". Scott was invited to the White House on Wednesday to discuss Trump's Charlottesville response as well as issues impacting minority communities.
McMaster didn't answer directly at a White House briefing whether Trump was revealing an intelligence assessment or whether he was just speculating.
A former adviser to Theresa May, Nick Timothy, responded to Trump's tweets nearly instantly, questioning whether it was based on actual intelligence.
Just hours after the Manchester attack, USA news outlets were citing U.S. officials claiming to identify the suspect before the Manchester police had released the information. "It is likely that law enforcement had been working on that problem set", McMaster said. After two terror attacks in the city in June, Trump seized on the moment. "Perhaps we are not almost tough enough".More news: New Equifax hassle: trying to buy iPhone X
Trump has a chance to widen the travel ban later this month.
The Supreme Court is scheduled to hear arguments on October 10 on the legality of the bans on travelers from six mostly Muslim countries and refugees anywhere in the world.
Currently, foreign nationals are banned from six countries - Iran, Syria, Sudan, Somalia, Libya and Yemen.More news: Entire Philippine city police off the job over killings, robbery
In an early morning tweetstorm, Trump slammed political correctness, as he once again made the case for his travel ban which continues to be fought out in the courts.
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