Khan had told London's citizens that there was no cause for alarm about increased police presence in the city in the coming days following an attack on the London Bridge that killed at least seven people.
Trump wrote. MSM referred to mainstream media.
In a Sunday tweet, Trump mischaracterized Khan's remarks by suggesting the mayor had said there was "no reason to be alarmed" about the attack itself.
In a series of early morning tweets, Trump urged the Justice Department to ask for an "expedited hearing" at the high court and seek a "much tougher version" of the order temporarily blocking entry to the us from a half-dozen majority Muslim countries.
The London attacks bring out the best in Britain and in Western leaders on the European continent; it brings out the worst in Trump and his followers.
In the wake of the London attack, Mr Trump has been tweeting about his stalled travel ban.
Earlier Sunday, Trump had criticized London's mayor after he sought to reassure residents about a stepped-up police presence following the attack, the third in the country in past three months, arguing on Twitter for leaders to "stop being politically correct" and focus on "security for our people".
"Just like terrorists are constantly evolving and finding new ways to disrupt us, harm us, attack us, the police and experts and all of us are finding new ways to keep us safe", Khan said in a Sunday statement.
"There can be no justification for the acts of these terrorists and I am quite clear that we will never let them win nor will we allow them to cower our city or Londoners", the mayor said in the interview.
"The United Kingdom stays in it and we believe it's an important worldwide agreement - so I'm not afraid to say when I think President Trump is getting things wrong". GOD BLESS!" But then he made a decision to slam the mayor of the city attacked, who had calmly warned his fellow Londoners: "Londoners will see an increased police presence today and over the course of the next few days.
The next day, Khan tells Amanpour that he isn't going to reply to the President's son.
After Trump's first attack on Khan, the acting U.S. ambassador to the UK, Lewis Lukens, notably singled out the London Mayor for praise.
In a highly unusual move, Muslim religious figures from across the country and from different schools of Islam said their pain at the suffering of the victims and their families led them to refuse to perform the traditional Islamic prayer - a ritual normally performed for every Muslim regardless of their actions.
After a spokesman for the Mayor said that he wouldn't respond to the comments o thee President, a number of news outlets ran articles critical of the Trump.
Trump has repeatedly twisted Khan's words on Twitter.
The President later returned to the London attack at an evening event at Ford's Theater, saying he had offered "unwavering support" to May in a phone call, before taking the chance to once again adopt his tough-on-terror posture.