The high court is weighing the administration's two emergency applications asking for the ban issued on March 6 to immediately go into effect. The March ban was Trump's second effort to impose travel restrictions through an executive order.
In a letter, Acting Solicitor General Jeff Wall said a ruling on Monday by the 9th US Circuit Court of Appeals in San Francisco means the government needs to file a new brief, which he proposed doing by June 15.
In an added dramatic twist, Trump himself plans to go to the Supreme Court on Thursday for the investiture of Justice Neil Gorsuch, an administration official said. Trump nominated Gorsuch in January. Gorsuch's confirmation by the US Senate in April restored the court's 5-4 conservative majority.
Trump's visit to the court would be his first since he became president on Jan. 20 and would put him face-to-face with the nine justices as they consider the fate of his travel ban unless the court acts before then. It is common practice for presidents to attend such events, which are purely ceremonial.