At issue is a ban Trump has said is necessary to protect Americans from terrorist attacks. Trump's proposed ban was a centerpiece of his 2016 presidential campaign. In other words, Trump'sMuslim ban, which is supported to last only 90-days, would go into effect.
The Supreme Court is the administration's final legal recourse. With this, the president is hoping to reverse the decisions of the lower courts.
The court weighs several factors when considering emergency applications.
Trumpissued his initial travel ban by executive order in January, but that measure caused chaos at airports and was quickly halted by the courts, prompting the administration to issue a new executive order with a narrower scope.
The challengers contest the administration's claim that urgent action is needed for national security reasons.
The Justice Department has filed two emergency applications arguing the ban on six mainly Muslim countries is necessary to keep the USA safe.
There will be "irreparable harm" if the stay is not granted.
The Court set a deadline of June 12, which comes about two weeks before its term is scheduled to end.
It was blocked after a legal challenge initially mounted by Washington state and Minnesota. However, in response to senators' questions about Trump's criticism of judges who had blocked his first immigration-related executive orders, Gorsuch said it was "disheartening" and "demoralising". That would limit the practical impact if the application were granted.
A major sticking point for the justices will be navigating how much discretion the president really has over immigration. He sometimes sides with the court's four liberals and could be the pivotal vote.
"It's an interesting procedural move, but the fact that it's taken this long may undermine, at least to some extent, the Trump administration's core argument that the entry ban, which has never gone into full effect, is essential to protect our national security", Steve Vladeck, a University of Texas Law school professor and CNN analyst, said.
A key part of the order a 90-day suspension of issuance of visas to citizens of six majority-Muslim countries (Iran, Libya, Somalia, Sudan, Syria and Yemen) is now blocked by two different district courts, one in Maryland and the other in Hawaii, the Politico reported. The order also placed a temporary moratorium on entry of refugees from any country while vetting procedures were reviewed.
A federal judge blocked it eight days later, an order that was upheld by a Ninth Circuit panel.
Virginia court of appealsruled the President's executive order is likely unconstitutional over religious discrimination because of Trump's campaign trail statements that he wanted to keep Muslims out of the US.
The 9th Circuit Court of Appeals heard arguments in the administration's request for a stay pending appeal to lift the Hawaii injunction on May 15, but it has not yet ruled.