Prime Minister Theresa May, the Conservative Party leader, was asked earlier on Monday about Trump's criticism of Khan.
Three jihadis first drove a van into pedestrians on London Bridge late on Saturday, before running into the bustling Borough Market area, where they slit peoples' throats and stabbed them indiscriminately.
"At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'"
"Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his "no reason to be alarmed" statement".
"But today US President renewed hostilities, accusing Khan of making a "pathetic excuse" and broadened his attack to include the press, claiming the "[mainstream media] is working hard to sell it!"
Ivanka Trump, Jared Kushner taking 'heads down' approach
McMaster have both discussed that, in general terms. back channels are an appropriate part of diplomacy", Spicer said. Kushner, is one of Trump's closest advisers.
When asked how relevant Trump's tweets are, White House spokeswoman Sarah Sanders said "they matter in the sense that they give him a communications tool" but said "the media obsesses over every period, dot".
Khan isn't paying any mind to Trump or his tweets right now because the mayor of London simply has "more important things to do".
"We must stop being politically correct and get down to the business of security for our people".
Khan said he had been too busy dealing with the fallout from the attack to respond directly to the tweet.
Meanwhile, Khan led a vigil of hundreds of Londoners in rememberance of those who died following Saturday night's terror attack in the capital.
New York City's mayor Bill de Blasio had already made his feelings known on Twitter, writing: "Mayor Sadiq Khan is doing an extraordinary job supporting Londoners in a time of pain. There's no reason to be alarmed".
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The Briton managed to quietly make his way from 12th on the grid to finish seventh and collect some valuable points for Mercedes . He said: "We couldn't plan much, but the plan was to pull away and as soon as the gap opened I took it".
Trump has leapt on the London attacks as evidence of the need for hardline security measures in the United States, including a "ban" on travelers from Muslim countries.
Mrs May, taking questions after a central London election campaign speech, was earlier asked if she wanted a period of silence from Mr Trump.
President Donald Trump lashed out at his own Justice Department Monday for seeking the Supreme Court's backing for a "watered down, politically correct version" of the travel ban he signed in March instead of a broader directive that was also blocked by the courts.
The two men have a history.
"By standing together as a city we will send a powerful message here and around the world - that Londoners will never be cowed by terrorism", Khan said.
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No. 17-seeded Roberto Bautista Agut led the lower-seeded winners, as his draw opened up after a four-set win over Aussie John Millman.