He assailed London Mayor Sadiq Khan for supposedly minimizing the threat, though what Mr. Khan said was that there was no reason to be alarmed by an enlarged police presence after the rampage.
May's Conservative government has worked closely with Khan, who represents the rival Labour party, she told the newspaper.
British Prime Minister Theresa May has said her USA counterpart's tweet about London Mayor Sadiq Khan immediately after last weekend's terror attack was "wrong".
Khan told broadcaster Channel 4 that Britain should not "roll out the red carpet" for Trump, while Liberal Democrat leader Tim Farron said May "must withdraw the state visit".
Mr Khan has called for the US President's planned state visit to the United Kingdom to be scrapped, but Mrs May has now said Mr Trump's controversial trip will go ahead.
President Donald Trump initially criticized Khan hours after the London Bridge attack and asserted that the mayor was downplaying the severity of the attack and its ramifications in the grand scheme of the battle against ISIS.
Trump accuses ex-FBI director Comey of cowardice over 'leaks'
"I believe the James Comey leaks will be far more prevalent than anyone ever thought possible", Trump wrote on Twitter on Sunday. Trump "feels completely and totally vindicated", and that "he is eager to continue to move forward with his agenda".
"[The president] appreciates Her Majesty's gracious invitation", Spicer responded, referring to the invitation extended to Trump by Queen Elizabeth.
A spokesperson for Mr Khan said the president had deliberately taken the comments out of context.
Trump Jr. continued defending his father and noted that every time media criticizes the president, their comments are proven to be wrong.
On Monday, he tweeted that Mr Khan's response was a "pathetic excuse" from a man who "had to think fast on his "no reason to be alarmed" statement".
"We keep saying, 'Okay, it's gonna be great.' We're gonna hold fast and we're gonna 'keep calm and carry on.' Maybe we have to keep calm and actually do something". The point is there is a reason to be alarmed.
In her interview with Sky on Tuesday, the prime minister asserted she had been "very clear" on what she thought about Presidents Trump's tweets. "[Mainstream media] is working hard to sell it!" tweeted Trump. Trump, meanwhile, said that "it is his ignorance to say that" and has raised questions about the approach of London's to confronting terrorism.
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