It was blocked by courts that found it was discriminatory.
But last night Trump's team filed two emergency applications seeking to block two different lower court rulings.
"We have asked the Supreme Court to hear this important case and are confident that President Trump's executive order is well within his lawful authority to keep the nation safe and protect our communities from terrorism," Justice Department spokeswoman Sarah Isgur Flores said in a statement.
At least five votes are needed on the nine-justice court in order to grant a stay.
The court has a 5-4 conservative majority, with Justice Anthony Kennedy - a conservative who sometimes sides with the court's four liberals - the frequent swing vote.
Another of the court's conservatives, Neil Gorsuch, was appointed by Trump this year.
In its 10-3 ruling, the U.S. 4th Circuit Court of Appeals
said challengers of the ban, including refugee groups and others represented by the American Civil Liberties Union, were likely to succeed on their claim that the order violated the U.S.Constitution's bar against discriminating against a particular religion.
The first, issued on January 27, led to chaos and protests at airports and in major U.S. cities before it was blocked by courts.
The second order was intended to overcome the legal issues posed by the original ban, but it was blocked by judges before it could go into effect on March 16.
