Trump, writing on Twitter Sunday, said: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is "no reason to be alarmed!"
But when Khan said in a statement that there was no cause for alarm, he was referring specifically to a visible increase in police activity on the streets of London in the wake of the attack.
"Londoners will see an increased police presence today and over the course of the next few days. There's no reason to be alarmed," he said.
Khan told CNN's Christiane Amanpour that the attack was "evil and cowardly" while also emphasizing that more police would be on the streets of London in the coming days.
A spokesman for Khan responded, calling Trump's tweet "ill-informed."
"The Mayor is busy working with the police, emergency services, and the government to coordinate the response to this horrific and cowardly terrorist attack and provide leadership and reassurance to Londoners and visitors to our city," the spokesman said. "He has more important things to do than respond to Donald Trump's ill-informed tweet that deliberately takes out of context his remarks urging Londoners not to be alarmed when they saw more police - including armed officers - on the streets."
The acting US ambassador to the UK, Lewis Lukens, issued a statement on Twitter singling out Khan for praise.
"I commend the strong leadership of the @MayorofLondon as he leads the city forward after this heinous attack," read a tweet from the US' London embassy attributed to Lukens.
Lukens is serving as ambassador until Trump gets a permanent pick confirmed. Trump has yet to formally nominate his choice for the job, although he said prior to his inauguratio
n that he would choose New York Jets owner Woody Johnson.
Trump's tweets have been heavily criticized by a number of British politicians, who are currently preparing for the country's general election which is scheduled to take place on Thursday.
Conservative politician Penny Mordaunt tweeted the transcript of Khan's interview and said: "I'm standing with resilient London and him."
Labour politician David Lammy said Trump's tweet was "cheap, nasty and unbecoming of a national leader."
Wes Streeting, another Labour politician, called for Trump's state visit to Britain to be canceled.
Trump was also fiercely criticized by Brendon Cox, the husband of former British lawmaker Jo Cox, who was murdered by a right-wing fanatic in November 2016.
"You represent the worst of your country, @SadiqKhan represents some of the best of ours," Cox wrote on Twitter.
In the US, Virginia Sen. Mark Warner, ranking Democrat on the Senate intelligence committee, said on CNN's "State of the Union" that he had also been troubled by Trump's tweets.
"I believe in many ways the Muslim-American community is better integrated into our society. I think that's always been our secret sauce here," Warner said. "That's why it troubles me so much to see the type of tweets the President has put out in the last 12 hours or so."
The White House did not respond to a request for comment on the criticism of Trump's tweets. But the President resumed his attack Monday morning.
"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!" he tweeted
Khan, London's first Muslim mayor, has long had a frosty relationship with Trump.
In 2015, Khan criticized Trump, saying he "doesn't have a clue about London" after the American claimed that certain areas of London were no-go zones.
Khan also lambasted Trump last year, claiming he held "ignorant views." Trump responded by labeling Khan "ignorant" and suggested the two should compete in an IQ test.
Then in January of this year, Khan insisted that Trump's state visit to Britain be canceled after the US President attempted to impose a travel ban on Muslim nations -- a policy which he labeled "cruel and shameful."
Trump's tweets came the day after he touted his so-called travel ban in the wake of the London terror attacks, while also pledging assistance to Britain.
Without referring explicitly to London, Trump wrote on his personal account: "We need to be smart, vigilant and tough. We need the courts to give us back our rights. We need the Travel Ban as an extra level of safety!"
Eight minutes later, he tweeted, "Whatever the United States can do to help out in London and the U. K., we will be there - WE ARE WITH YOU. GOD BLESS!"
Cecillia Wang, the deputy legal director of the American Civil Liberties Union, quickly accused Trump of exploiting the situation.
"We need to be outraged when the president exploits a terrible violent crime to push his discriminatory and illegal policy," she tweeted
And Kentucky Secretary of State Alison Grimes, a Democrat, said Trump was stoking "fear and hate" with his response.
"Our Commander in Chief should be directing support to a vital US ally, not using horrendous attack to stoke fear & hate," she tweeted
Earlier, Trump retweeted the Drudge Report when it referred to "fears of a new terror attack," although the nature of the incidents had not yet been confirmed by authorities. Shortly after Trump tweeted, British Prime Minister Theresa May said the incident was being treated as a "potential act of terrorism" and London police later tweeted that they were "declared as terrorist incidents."
White House press secretary Sean Spicer said Trump had been briefed on the situation by his national security team. A spokesman for Vice President Mike Pence said he also has been briefed and spoke with Trump from Air Force Two.
Pence also tweeted, "Our thoughts & prayers are w/ the victims, courageous first responders & all the people of London. As President Trump said: WE ARE WITH YOU."
A van mowed down pedestrians
as it sped down London Bridge in the British capital Saturday night, leaving bodies lying in the roadway, a witness to the incident told CNN.
Also Saturday, a man with a "massive knife" entered a restaurant at Borough Market, just south of the bridge, and stabbed two people inside, a witness told CNN.
Trump's travel ban -- which, among other things, would temporarily block entry into the US from six Muslim-majority countries -- has been blocked by a number of federal court decisions. On Thursday, the Trump administration asked the Supreme Court
to allow the ban to go into the effect while the court considers its legality.