On Friday, the Supreme Court asked the challengers of the travel ban to file responses to the emergency request by June 12.
The tweets also threaten to overshadow a series of White House policy announcements on infrastructure this week.
The administration filed emergency applications with the justices seeking to block lower court rulings that went against Trump's order barring entry for people from Iran, Libya, Somalia, Sudan, Syria and Yemen for 90 days while the US government implements stricter visa screening.
A key issue before the justices in whether Trump's comments during the 2016 president campaign, including calling for "a total and complete shutdown of Muslims entering the United States", can be used as evidence that his order was meant to discriminate against Muslims.
A federal appeals court in Virginia also ruled against the administration, saying despite the changes, the revised ban "drips with religious intolerance, animus, and discrimination".
James Comey: la Russie s'est ingérée dans les élections américaines
Des proches sont ciblés, notamment son gendre, Jared Kushner, ou son ancien directeur de campagne, Paul Manafort, mais M. Mais cette fois, il en a ressenti le besoin, car il ne pouvait pas enregistrer les conversations.
"The Justice Dept. should have stayed with the original travel ban, not the watered down, politically correct version they submitted to S.C.", Trump tweeted, referring to the country's highest court.
Most who have used a smart phone were not confused by President Donald Trump's recent use of the "word" covfefe in a tweet, mistyping happens.
Neal Katyal, an attorney for the state of Hawaii in its challenge to the executive order, embraced the president's tweets on Monday morning.
"The Justice Dept. should ask for an expedited hearing of the watered down Travel Ban before the Supreme Court - & seek much tougher version!" the president said.
In later Twitter messages, George Conway emphasized he still "very, very strongly" supports Trump and his executive order, but he said tweets on legal matters "seriously undermine" the administration's agenda.
Last week, his administration rolled out new policies for those seeking a USA visa, asking for the social media handles they have used over the last five years and biographical information going back 15 years. But Trump on Monday was having none of it. Wednesday, he'll visit Cincinnati to focus attention on the nation's inland waterways. Most of the states had also backed Trump earlier in the litigation.
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