Khan had actually sought to reassure the capital's residents and workers over the increased presence of armed police on London's streets.
The three suspects were shot dead by police officers within minutes after they drove a van into pedestrians on the bridge and then stormed pubs and restaurants, stabbing anyone in their path. After Trump's criticism, one of the mayor's spokesmen said in response to Trump's tweets that Khan had "more important things to do" in terms of overseeing the city's response and recovery.
Mr Khan's spokesperson had described the first round of presidential tweets as "ill-informed" - and said they had deliberately taken his remarks out of context.
Trump mocked Khan's comment on Sunday, suggesting in a tweet that the mayor was downplaying the attacks. "MSM [Mainstream media] is working hard to sell it!" the president wrote.
Khan's remarks about not being alarmed referred to the heightened police presence in the city, not with the threat of terrorism itself. While speaking out his mind about the "security of his people" after the London Bridge terror incident, he said, "We must stop being politically correct and get down to the business of security for our people".
However, Khan is stressing that policy divisions are harmful and should be acknowledged, yet he pays lip service to the "special relationship" between the US and England, which stands firm even while Trump's acting like a persistent, insult-tossing mosquito.
At the fund-raiser Trump said he would do whatever was necessary to protect the United States from a "vile enemy" that had waged war on innocents for too long. He calmly explained his opposition to Trump's proposed travel ban on visitors from several Muslim countries. He said on Twitter that others "can call it whatever they want, but I am calling it what we need and what it is, a TRAVEL BAN!"
"Maybe rather than the mayor of London attacking, maybe he should do something about it", Trump Jr. said.
"These tweets may make some ppl feel better", George Conway said on Twitter, but "certainly won't help" get five votes on the Supreme Court.
Mr Trump later called Prime Minister Theresa May to offer his condolences.
Trump and Khan have spent the past year sniping at one another, largely over Trump's proposed travel ban that would temporarily bar some Muslims from entering the United States.
"We need to be smart, vigilant and tough", he tweeted.
"It's not just about resource, it's about the powers people have", May said at a campaign event in central London on Monday.
"We saw on Saturday night some of the people in the health service, some of the consultants, surgeons, were Muslims surgeons, some of them people who'd come to this country from Muslim majority countries", the mayor continued.