Speaking to Channel 4 News, Khan said: "I don't think we should roll out the red carpet to the president of the USA in the circumstances where his policies go against everything we stand for.
"When you have a special relationship it is no different from when you have got a close mate. You stand with them in times of adversity but you call them out when they are wrong. There are many things about which Donald Trump is wrong."
There are plans for Trump to take part in a state visit in October. This was originally billed for June, but concerns had been raised about the size and scale of protests that could take place.
Protests have been a regular feature wherever Trump has visited, both at home and abroad, many of these seeing tens of thousands of people take to the streets.
At an election press conference on Monday (5 June), Theresa May defended Khan saying that he was doing a "good job" following the attack.
At the White House press briefing on Monday, the deputy press secretary, Sarah Huckabee Sanders said: "I don't see that the president is picking a fight with the mayor London", she then went on the blame confusion on "media spin."
Over the weekend, Trump said: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!"
In a separate tweet on Monday, Trump said: "Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his 'no reason to be alarmed' statement. MSM is working hard to sell it!"
Seven people died on Saturday and dozens more were injured when a van being driven southbound on London Bridge rammed into pedestrians. Three attackers, armed with knives and wearing fake suicide jackets, exited the van and entered the nearby Borough Market, stabbing various people before eventually being shot dead by police.