Several British lawmakers have called on UK Prime Minister Theresa May to cancel a scheduled state visit for President Donald Trump following his criticisms levelled against Mayor Sadiq Khan of London.
Khan's staff said he was too busy to respond to Trump's tweets.
A spokesman for the London mayor derided Trump's statement as an "ill-informed tweet that deliberately takes out of context his remarks urging Londoners not to be alarmed when they saw more police - including armed officers - on the streets".
"MSM (mainstream media) is working hard to sell it!"
May declined to directly criticize Trump for his tweet, which has prompted a fierce backlash in Britain.
The latest deadly terrorist attack on one of America's most important allies drew a fitting initial response from President Trump: "Whatever the United States can do to help out in London and the U.K., we will be there", he tweeted.
Trump's tweet renews his mischaracterization of Khan's statement to London residents following a vehicle and knife attack that left seven people dead and dozens injured.
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The ex-LBC radio host has appeared on the Fox News channel in the wake of the attack on Saturday night, on a programme that Trump is known to watch religiously.
Trump, in the aftermath of an attack in San Bernardino, California, calls in a statement for a "total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what the hell is going on".
The White House on Monday denied suggestions from US reporters that Trump "picked a fight" with Khan "because he was Muslim".
While attending a fundraiser for Rep. Elijah Cummings' (D-Md.) youth program, she added, "It is time for steady, determined leadership like we are seeing from London's mayor and local authorities".
"I think Sadiq Khan is doing a good job and it's wrong to say anything else - he's doing a good job", she said at a press conference.
"It is a reality I'm afraid that London, New York, other major cities around the world have got to be prepared for these sorts of things", he said.
"We're working with him, working together and that's important - central government and the London mayoralty and his officials working together to ensure we are responding to the attack and looking, as I said earlier, at the work that the police is doing to give the public extra protection and extra reassurance".
Asked what it would take for her to publicly criticize the US President, May suggested that she "was not afraid" to speak out when Trump "gets things wrong".