Trump accused Khan of making a "pathetic excuse" over his statement urging Londoners not to be alarmed by the presence of additional police on the streets in response to the attack.
But British Prime Minister Theresa May said Khan was doing a "good job", echoing public sentiment across London.
Three jihadis drove a van into pedestrians on London Bridge on Saturday night before running into the bustling Borough Market area where they slit people's throats and stabbed them indiscriminately. Police shot dead all three attackers.
Khan had said on Sunday morning that people would see an increased police presence on the streets of the capital and should not be alarmed by that.
Trump mocked Khan's comment on Sunday, suggesting in a tweet that the mayor was downplaying the attacks. A spokesman for Khan responded that the mayor "has more important things to do than respond to Donald Trump's ill-informed tweet that deliberately takes out of context" his remarks.
Trump's comments drew widespread scorn in Britain but the U.S. leader went on the attack again on Monday, saying in a tweet: "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!" Trump wrote. MSM referred to mainstream media.
White House spokeswoman Sarah Sanders said she did not think it was fair to characterise Trump's tweets as "picking a fight" with Khan, who is the first Muslim elected as London mayor.
"The point is, there is a reason to be alarmed. We have constant attacks going on, not just there but across the globe, and we have to start putting national security and global security at an all time high," she told a White House briefing.
Khan said he had been too busy dealing with the fallout from the attack to respond directly to the tweet.
Khan, who belongs to the opposition Labour Party, is popular in London and his response to Saturday's killings has been widely praised as dignified.
Prime Minister May, the Conservative Party leader, was asked earlier on Monday about Trump's criticism of Khan.
"I think Sadiq Khan is doing a good job and it is wrong to say anything else," she said.
Khan's statement on Sunday morning condemned the attack and gave a number of details about what had happened and what measures were being taken in response.
"Londoners will see an increased police presence today and over the course of the next few days. No reason to be alarmed. One of the things the police, all of us need to do is make sure we're as safe as we possibly can be," Khan said.
Not the first clash
In his Sunday tweet, Trump commented: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'"
It was met with a barrage of criticism in both Britain and the United States, with former Vice President Al Gore among many public figures who accused Trump of misrepresenting what Khan had said.
A YouGov poll of 1,000 Londoners published on Monday found that Khan was more trusted than both May and national Labour leader Jeremy Corbyn to make the right decisions about keeping Britain safe from terrorism.
"My focus from Saturday night has been working with the police the emergency services and the government to deal with the horrific attack on Saturday," Khan told Sky News, when asked about Trump's latest tweet.
"I just haven't got time to respond to tweets from Donald Trump. I've got better and more important things to focus on."
The two men have history. During the U.S. presidential election campaign, Khan was among many people who spoke out against Trump's proposed ban on Muslims entering the United States, an idea he said would play into the hands of extremists.
During a visit to Chicago in September last year, Khan endorsed Trump's opponent Hillary Clinton.
In March, after an attack by an Islamic militant that left five people dead in Westminster, central London, Trump's son Donald Trump Jr. issued a tweet that criticised Khan.
Trump Jr. wrote "You have got to be kidding me?!" above a link to an article reporting comments Khan had made months earlier.
In the article, Khan was reported as saying that being prepared for terror attacks was "part and parcel" of living in a major city.
