The pair publicly clashed in the latest round of exchanges as the US head of state began a three-day state visit to the UK.
On Sunday, Mr Khan described the president as “just one of the most egregious examples of a growing global threat” compared his language to that used by fascists but as Mr Trump landed in the UK on Monday, he launched a trademark Twitter broadside at Mr Khan.
But how many fallouts has there been?
Misspelling the London mayor’s name, he said Mr Khan has “by all accounts done a terrible job” and has been “foolishly ‘nasty’ to the visiting president of the United States”.
“He is a stone cold loser who should focus on crime in London, not me,” Mr Trump tweeted.
“…Kahn reminds me very much of our very dumb and incompetent Mayor of NYC, de Blasio, who has also done a terrible job – only half his height.
“In any event, I look forward to being a great friend to the United Kingdom, and am looking very much forward to my visit.”
Reacting to the comments, a spokesman for Mr Khan said that “childish insults” should be “beneath the president of the United States”.
Mr Trump laid into Mr Khan after a wave of terror attacks in the capital the previous year, accusing him of “doing a terrible job” and a “bad job on crime”.
The verbal attack on Mr Khan came after the London mayor refused to block a plan to fly a giant inflatable “Trump baby” near Parliament to coincide with the US president’s visit to the UK.
Flown in London during the president’s last visit, the 20ft high blimp depicted the US leader as an angry infant wearing a nappy and clutching a mobile phone.
At the time, Mr Khan said he would not rise to Mr Trump’s “beastly” comments.
The pair clashed in the wake of the deadly London Bridge terror attack, after Mr Khan said Londoners should not be alarmed by visibly increased security on the streets of the capital.
In response, Mr Trump tweeted: “At least 7 dead and 48 wounded in terror attack and Mayor of London says there is ‘no reason to be alarmed!’”
Mr Khan said he would not allow Mr Trump or anyone else to “divide our community”.
Before Mr Trump was elected as US president, he and Mr Khan were involved in another public row.
The then presidential candidate had previously called for Muslims to be banned from the US, but after the election of Mr Khan as mayor, said he would make an exception for him.
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In response, Mr Khan, who is a Muslim, said he is “not exceptional”, adding that the views of Mr Trump and his advisers on Islam are “ignorant” and invited him to come and meet moderate Muslims.
He added: “The vast, vast, vast majority of Muslims are law-abiding and peaceful (and) unequivocally condemn these acts of terror committed by a small number of people using the name of Islam to justify their nihilistic actions.”
Hitting back during an interview, Mr Trump branded the statements from the Labour politician as “very rude” and “very nasty”, and challenged him to an IQ test.