The foreign secretary said there was “no reason” to rescind Mr Trump’s invitation despite the Republican billionaire branding one of the mayor’s statements on the terror attack “pathetic”.
But Mr Johnson, the former Mayor of London, said the pair were able to “stick up for themselves”.
Speaking on the Today Programme on BBC Radio 4, he added Mr Khan was correct to reassure the public after the attack.
“As Mayor of London, Sadiq was perfectly right to reassure the public about the presence of armed officers on the street.”, he said.
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Boris Johnson said Mr Trump's planned visit should not be rescinded after his London attack tweets
The invitation has been issued and accepted and I see no reason to change that
Pushed on whether the President’s invite should be rescinded, he said: “The invitation has been issued and accepted and I see no reason to change that but as far as what Sadiq Khan has said about the reassurances that he’s offered the people of London, I think he was entirely right to speak in the way that he did.
“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 Prime Minister 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!”
Morning after London attack: Heightened police presence at Borough Market & Bridge Sun, June 4, 2017
SIX people have been killed after a horrific terror attack targeted London Bridge and Borough Market on Saturday night. These are the pictures are London wakes up to the tragic scenes
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The online feud came after Mr Trump, during a series of tweets following the London Bridge terror assault, misrepresented Mr Khan’s statement that there was “no reason to be alarmed” when seeking to reassure Londoners about an increased police presence.
In round two of his attack, Donald Trump accused Mr Khan – London's first Muslim mayor – of offering a "pathetic excuse" for the comments about policing in response to Saturday's attack, which left seven people dead.
Mr Khan had tried to encourage Londoners to be calm in the coming days.
But his words were used by Mr Trump as evidence of the need for "extreme vetting" of Muslims and hardline security measures in the United States, including a "ban" on travelers from Muslim countries.