Trump's taunting of Khan, one of Britain's most prominent Muslims, started within hours of the attack that left seven people dead and dozens injured after the mayor appealed for calm, referring to the increased presence of armed police on the streets. He was clear to note the conditional nature of his rejection of Trump, telling the British broadcaster, "When you have a special relationship, it is no different from when you have got a close mate".
It is not the first time a call has been made to rescind Trump's invitation to visit the United Kingdom, as two million people signed a petition in January calling for a temporary "POTUS ban".
His tweet took Khan's comment that Londoners had "no reason to be alarmed" about the increased police presence out of context. On the topic of the state visit, which is proposed for later this year, Khan said his position remains the same.
Khan's spokesperson also said that the Mayor has priorities to attend to rather than reply to Trump's "ill-informed tweets". "(Mainstream media) is working hard to sell it!"
"I just haven't got time to respond to tweets from Donald Trump". And as the president of the world's superpower, Mr Trump should be advised to do the same: to think before he tweets.
Khan, a human rights lawyer and practicing Muslim hails from Pakistan, has challenged repeatedly Trump's calls to ban Muslims or people from Muslim countries from entering the U.S, saying the president has a "rude view of Islam".More news: At least 18 killed in Mogadishu restaurant attack
Asked about the spat with Mr Trump, Mr Khan told ITV1's Good Morning Britain: "We're not kids in a playground, he's the president of the US".
"Mark it all down as further evidence that the most effective opponent of the Trump presidency is Donald J. Trump".
Reuters/Clodagh KilcoyneMayor of London Sadiq Khan visits the scene of the attack on London Bridge and Borough Market. "One of the things the police, all of us need to do is make sure we're as safe as we possibly can be", Khan said.
Politicians have urged Prime Minister Theresa May to withdraw Trump's invitation over his criticism of Khan.
Khan said London should not host an allied leader who suggested the mayor had refused to stand with his city in the aftermath of a horrific attack.
The acting US ambassador to the UK, Lewis Lukens, pointedly singled out Khan for praise.
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.