The story is about Trump's response to Saturday's terror attack in London which saw seven people killed as three extremists ran into pedestrians with a van and then went on a stabbing rampage in a popular area of the city.
Mr Khan has called for the US President's planned state visit to the United Kingdom to be scrapped, but Mrs May said Mr Trump's controversial trip would go ahead. On Sunday Trump leveled an inaccurate criticism of London Mayor Sadiq Khan, saying the mayor was telling people there was "no reason to be alarmed" about the attack.
To huge applause, Mr Khan told those gathered for the service in Potters Fields Park, near London's City Hall: "As a proud and patriotic British Muslim I say this you do not commit these disgusting acts in my name".
Khan never responded directly to Trump's tweets-his spokesperson explained that the mayor had "more important things to do".
And some Labour Party candidates and parliamentarians called for Trump's state visit to the United Kingdom later this year to be cancelled, the BBC reported.
Trump took the statement out of context, and claimed that Khan had said people should not be alarmed by terrorism.
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He continued, "When you have a special relationship it is no different from when you have got a close mate".
Trump's latest tweet came after he conceded that his administration's executive order temporarily suspending visa issuance to citizens of six majority-Muslim countries is indeed "a TRAVEL BAN!" and blasted his own Justice Department for revising his original order. "Why would you want to stop them coming?" "We are not going to let Donald Trump divide our communities".
Trump has repeatedly twisted Khan's words on Twitter.
He has asked British prime Minister Theresa May to withdraw the offer of a state visit by Trump.
Mr Khan, a Muslim, has previously criticised the president's plans to temporarily restrict travel to the U.S. from six mainly Muslim countries.
The Trump administration is expected to take the proposal to the Supreme Court next week.
"I think Sadiq Khan is doing a good job and it's wrong to say anything else - he's doing a good job", she told a press conference on Monday.
"London stands in defiance against this cowardly attack on our city, our people, our values and our way of life".