Opponents of the ban, who had persuaded the two appeals courts to block the executive order, said the court should continue to review the cases.
The court did not act on a separate challenge brought by the state of Hawaii, which the court had also agreed to hear.
The court has not yet announced whether it plans to hear the other challenge to the order brought by the state of Hawaii regarding Trump's ban stopping the refugee resettlement program in the US for 120 days.
"Because that provision of the order "expired by its own terms" on September 24, 2017, the appeal no longer presents a 'live case or controversy", the Supreme Court said. The refugee restrictions are set to expire on October 24, and the case is also likely to be dismissed as moot when that happens, according to the press coverage.
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New challenges already have been filed against the new travel policy and could return to the court.
On Tuesday, the Supreme Court dismissed the ban on majority-Muslim countries. After the ban's 90-day time limit expired, the court decided the case should expire too. "And the government urged the court to vacate the lower courts' decisions, so that they would not carry any legal weight in the future, describing such a step as essential to avoid "'legal consequences' in future cases, on critical issues including justiciability and the President's authority to protect national security".
The 4th Circuit case was brought by the International Refugee Assistance Project, which argued that banning travel from six majority-Muslim countries violated the First Amendment's guarantee of freedom of religion. Another case that is pending from the Ninth Circuit is also likely to be vacated.
In some ways it is more expansive than the second executive order it replaced - remaining in effect indefinitely and imposing restrictions on eight, rather than six, countries. Justice Sonia Sotomayor was the only justice to note her disagreement with this outcome; she would have dismissed the case as improvidently granted. But unlike the previous ban, the restrictions vary from place to place, and countries that increase their cooperation and information-sharing with the United States might be able to find their way off the list.