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 USA from a half-dozen majority Muslim countries.
It's unclear whether the president has conveyed his requests to the Justice Department, which he oversees, in a forum other than Twitter.
"We stand together tonight to honour the memories of the innocent lives lost and people injured in the barbaric attack on our city".
As the terrorists attacked, eyewitnesses claimed that the terrorists shouted "This is for Allah".
After that order was struck down by the courts, the administration chose to write a second directive rather than appeal the initial ban to the Supreme Court. The second order removed Iraq from the list of banned countries. "This bloodshed must end, this bloodshed will end", he vowed. "He is more of a statesman than Trump will ever be".
Trump and the Mayor have clashed before, when Mr Khan said that as a Muslim he didn't want to be "the exception" to the President's travel ban. He previously had commented via a series of Twitter posts Saturday. "And this president is trying to do something to protect the people of this country".
Khan received support from many, including Prime Minister Theresa May.
"Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his "no reason to be alarmed" statement". Khan's spokesman said he was too busy to respond to Trump's "ill-informed" tweet. "There's no reason to be alarmed".
Khan had actually sought to reassure the capital's residents and workers over the increased presence of armed police on London's streets. "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. She stopped short of directly criticising the United States president. "If we don't get smart it will only get worse". Police shot dead all three attackers. You are the best of us. "That's because they used knives and a truck!"
"We're working with him, working together and that's important - central government and the London mayoralty and his officials working together to ensure we are responding to the attack and looking, as I said earlier, at the work that the police is doing to give the public extra protection and extra reassurance".
Trump's first comment after the attack came late Saturday on Twitter. Still, the courts have also blocked that directive.
Khan has reportedly also said Trump was wrong about "many things" and that his state visit to the United Kingdom should not go ahead. Trump Jr.'s tweet was a response to attacks near Westminster Palace.