He accused Mr Khan of offering a “pathetic excuse” for saying there was no reason for people to be alarmed.
Mr Khan had in fact said people should not be alarmed by an increased police presence.
After a vigil for the victims of the attack, Mr Khan said he would not allow Mr Trump to “divide our communities”.
Seven people were killed and 48 others injured in the attack on Saturday.
Mr Trump took issue with Mr Khan’s statement in the aftermath of the attack, when the mayor said: “Londoners will see an increased police presence today and over the course of the next few days. No reason to be alarmed.”
The US president responded: “At least 7 dead and 48 wounded in terror attack and Mayor of London says there is ‘no reason to be alarmed!'”
He followed this up with another tweet on Monday, saying: “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!”
The mayor’s spokesman earlier made clear that he was telling Londoners not to be worried about the increa
Speaking to the BBC after the vigil, Mr Khan said: “We’ve got to recognise that some people want to divide our communities, some people thrive on fuelling division.
“That’s not me, that’s not the London I know, and we aren’t going to allow anybody, whether it’s Donald Trump or anybody else to divide our community.”
His spokesperson earlier said he “has more important things to do than respond to Donald Trump’s ill-informed tweet that deliberately takes out of context” the mayor’s remarks.
Calls to withdraw London invite
Mr Trump’s attacks on Mr Khan have drawn condemnation from both sides of the Atlantic.
His critics have accused him of being insensitive and twisting the mayor’s words.
Politicians in the UK on Monday called on the prime minister to withdraw the invitation for Mr Trump’s state visit later this year.
The leader of the Liberal Democrats, Tim Farron, said: “This is a man insulting our national values at a time of introspection and mourning.”
Over the weekend, Prime Minister Theresa May refused to criticise Mr Trump, simply saying that Mr Khan was doing a “good job”.
British voters go to the polls on Thursday in a general election.
“Try to imagine the UK prime minister attacking the Mayor of NYC the day after 9/11,” said European Parliament cabinet member Simon O’Connor.
US mayors back Khan
New York Mayor Bill de Blasio was quick to defend Mr Khan, praising him for “doing exactly the right thing”.
“I don’t understand why Donald Trump is trying to undermine a man who’s trying to protect the people of London. It makes no sense,” Mr de Blasio told the BBC’s Nick Bryant during a press conference in New York on Monday.
The US Conference of Mayors, representing more than 1,400 American cities, backed Mr Khan.
“He has risen above this crisis of death and destruction, as mayors continue to do, to alleviate fear, to bring comfort to his people of London,” the mayors wrote in a statement.
Mr Khan, a Muslim, has previously criticised the president’s plans to temporarily restrict travel to the US from six mainly Muslim countries.
After Mr Trump as a presidential candidate announced his plan, Mr Khan told the BBC he hoped he would lose “badly” , adding that he was a “buffoon”.
He also called Mr Trump’s views on Islam “ignorant”, leading the New York billionaire to challenge him to an IQ test.
In the wake of the London attack, Mr Trump has been tweeting about his stalled travel ban.
Federal courts struck down the first proposal in January. The administration replaced it with a less stringent version order in March, but that also ended up in limbo after legal defeats.
On Monday, the president attacked the Justice Department for revising the original measure, leaving it “watered down” and “politically correct”.
The Trump administration is expected to take the proposal to the Supreme Court next week.
He argues the measure is needed to prevent attacks in the US, but critics say the policy is discriminatory and has little national security justification.
This article was 1st published by BBC