On Sunday, Trump mocked Khan's statement asking Londoners not to be alarmed, suggesting in a tweet that the mayor was downplaying the attacks. "MSM is working hard to sell it!"
On Saturday evening, a vehicle drove into pedestrians on London Bridge and attackers stabbed several people at London's Borough Market.
Khan had said in one of his first statements in reaction to the attack that people would see an increased police presence on the streets of the capital and should not be alarmed by that.
Trump is due to be granted a formal state visit to the United Kingdom in October but has in recent days embarked in a series of Twitter attacks on Khan.
"When you have a special relationship it's no different to when you've got a close mate, you stand with them in times of adversity but call them out when they're wrong and there are many things about which Donald Trump is wrong".
In fact, Trump's tweets contradicted statements made by the U.S. embassy in London, resulting in the acting ambassador to the UK, Lewis Lukens, receiving a barrage of online abuse from Trump supporters.
A day after bombings in NY and New Jersey, Khan tells The London Standard that attacks are "part and parcel" of life in major cities.
Khan previously called for the visit to be cancelled following Trump's travel ban on mainly Muslim countries in January.More news: 2 children shot, injured on Chicago playground
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"It's extraordinary that Trump from cavernous depths of his scientific ignorance is prepared to challenge conclusions of 97 percent of the world's experts on this matter", said Paul Flynn, Labour Party Parliament member.
May said Khan has been doing "a good job" in the aftermath of Saturday's London Bridge attack.
Trump tweeted another round of criticism Tuesday morning. "It happened again, and we keep appeasing it, and we keep saying OK it's going to be great, we're going to hold fast, and we're going to keep calm and carry on". That's not what I said.
"The Mayor is busy working with the police, emergency services and the government to coordinate the response to this horrific and cowardly terrorist attack and provide leadership and reassurance to Londoners and visitors to our city".
British Foreign Secretary Boris Johnson said on Tuesday he saw no reason to cancel Donald Trump´s state visit.
Khan knows that Trump's tweets have partially served to reinforce the preexisting conflict between the two men.
The U.S. ambassador to Qatar is also on the spot this week after Trump linked Qatar on Twitter with the "funding of Radical Ideology" and seemingly took sides with Saudi Arabia in Monday's diplomatic flare-up with Qatar.