The court announced yesterday a deadline of 3:00 PM on June 12 to address the Justice Department's filings on Thursday night urging the high court to review the legality of the travel ban and to allow it to go into force while the litigation goes forward.
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 currently blocked by two different district courts, one in Maryland and the other in Hawaii, the Politico reported.
The Hawaii order also blocked a 120-day halt Mr Trump planned to refugee admissions to the US from around the globe. Last week, the 4th Circuit Court of Appeals voted, 10-3, to uphold the Maryland-based judge's injunction.
A three-judge panel of the 9th Circuit is considering the Hawaii injunction but has not yet ruled on it.
Mr Trump's March order was his second go-round on the travel ban. The first one, issued in January, was quickly halted by courts after the initial implementation of the directive prompted chaos at various US airports.
After the 9th Circuit failed to revive the order, Mr Trump decided to re-draft it rather than taking the issue to the Supreme Court at that time.
The Donald Trump administration had yesterday urged the SC to reinstate its travel ban, elevating a divisive legal battle involving national security and religious discrimination.