Speaking on radio station LBC, the London mayor said he had “no time” to be “bothered” about the Republican billionaire as he refused to be drawn into a further spat.
Mr Trump branded one of the mayor’s statements on the London Bridge terror attack “pathetic” and has sent a series of critical tweets.
Mr Khan has said the President should not be afforded a state visit to the UK and that he should use his time more wisely.
“I made the point that state visits are given to leaders for a number of criteria and I couldn’t think of one that was worthy of him having a state visit,” he said.
“I didn’t think we should roll out the red carpet. Nothing’s changed my mind about that. I’m the Mayor of London, not the President.
Sadiq Khan said Donald Trump should stop "obsessing" over him
I just think he should find things to do rather than being obsessed about me
“As the Mayor of London, since Saturday I’ve been working with the police, with emergency services, with the Government, to deal with the aftermath of the horrific attacks.
“I haven’t had time to even give it a moment’s thought what Donald Trump’s tweeting.
“But in my normal course of a working week, whether it’s grappling with air quality, whether it’s tackling the housing crisis, whether it’s providing affordable transport, or working with the police to keep our city safe.
"I haven’t got time to be bothered about Donald Trump and I just think he should find things to do rather than being obsessed about me.”
President Donald Trump makes historic visit to Israel Mon, May 22, 2017
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President Trump and his contingent arrived for a 28-hour visit to Israel and the Palestinian Authority areas on his first foreign trip since taking office in January
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US President Donald Trump visits the Western Wall, the holiest site where Jews can pray, in Jerusalems Old City on May 22, 2017
He said: “I don’t wish to enter into a row between those two individuals who I think probably are perfectly able to stick up for themselves. I know them both.”
The American president picked a fight on the social media platform with Mr Khan and continued it just hours after Theresa May said it was wrong for the American to have criticised him.
Mr Trump tweeted: “Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his "no reason to be alarmed" statement. MSM [mainstream media] is working hard to sell it!”