The current ban initially restricted travel from eight nations — Iran, Libya, Syria, Yemen, Somalia, Chad, Venezuela and North Korea — six of which were predominantly Muslim. Chad was recently removed from the list.
The restrictions vary in their details, but, for the most part, citizens of the countries are prohibited from immigrating to the United States, and many are barred from working, studying or vacationing here.
In December, in a sign that the Supreme Court may uphold the latest order, the court allowed it to go into effect as the case moved forward. The decision effectively overturned a compromise in place since last June, when the court said travelers with connections to the United States could continue to travel here notwithstanding restrictions in an earlier version of the ban.
Justices Ruth Bader Ginsburg and Sonia Sotomayor dissented from the December ruling.
Hawaii, several individuals and a Muslim group challenged the latest ban’s limits on travel from the predominantly Muslim nations; they did not object to the portions concerning North Korea and Venezuela. They prevailed before a Federal District Court there and before a three-judge panel of the United States Court of Appeals for the Ninth Circuit, in San Francisco.
The appeals court ruled that Mr. Trump had exceeded the authority that Congress had given him over immigration and had violated a part of the immigration laws barring discrimination in the issuance of visas.
In a separate decision that is not directly before the justices, the United States Court of Appeals for the Fourth Circuit, in Richmond, Va., blocked the ban on different grounds, saying it violated the Constitution’s prohibition of religious discrimination.
The Supreme Court said it would consider both the statutory and constitutional questions when it agreed to hear the case.
Lawyers for the challengers have said Mr. Trump’s own statements provided powerful evidence of anti-Muslim animus. The latest order, they said, was infected by the same flaws as the previous ones.