Just hours after the attack, Trump tweeted: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'".
Khan had told Londoners there was "no reason to be alarmed" about an increased police presence in the coming days.
In January of this year, Khan insisted Trump's state visit to Britain be canceled after the US President attempted to impose a travel ban on Muslim nations - a policy that he labeled "cruel and shameful". His comments caused outrage among British officials.
Speaking to Britain's Channel 4 News on Monday, Khan said the U.S. President was wrong about "many things". "There are many things about which Donald Trump is wrong". Cancel the state visit and tell Trump where to get off.
The Prime Minister said party politics should be "put to one side" after the USA president blasted Sadiq Khan in tweets that were widely condemned by politicians of all stripes.
The foreign secretary also said this morning the row between Khan and Trump was "trivial".
He told BBC Radio 4's Today programme: "The invitation has been issued and accepted and I see no reason to change that".
Police said authorities killed Khuran Shazad Butt, 27, Rachid Redouane, 30, and one other man after they jumped out of a hired van that had slammed into pedestrians on the London Bridge late Saturday and stabbed multiple people at nearby Borough Market.
"It's somewhat freakish the way the president went after the mayor", said Senator Ben Cardin, (D) Maryland.
We have a special relationship and we should work closely with the Americans.
"I'm very clear that Sadiq is doing a good job as mayor of London, we are working with him, working together".
"We write on behalf of individuals who have been blocked from your most-followed Twitter account, @realDonaldTrump, because they disagreed with, criticized, or mocked you or your actions as president", the Knight Institute letter reads.
FACTS: Trump's tweet directly contradicted an earlier statement by his homeland security secretary that the travel restrictions blocked by US courts do not constitute a ban.
Suhaib Webb - an imam who leads Center DC, which has a large online youth following - said he is angry that the president and those close to him are "quick to pull the trigger on anything that has to do with Islam or involves a person of color".