CreditVictor J. Blue for The New York Times
The restrictions vary in their details, but for the most part, citizens of the countries are forbidden from emigrating to the United States and many of them are barred from working, studying or vacationing here.
In December, in a sign that the Supreme Court may be more receptive to upholding the September order, the court allowed it to go into effect as the case moved forward. The move effectively overturned a compromise in place since 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 six 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 Congress had given him over immigration and had violated a part of the immigration laws barring discrimination in the issuance of visas.
In his brief urging the Supreme Court to hear the case, Solicitor General Noel J. Francisco wrote that the president has vast constitutional and statutory authority over immigration. He added that the third order had been the result of “an extensive, worldwide review by multiple government agencies.”
“The courts below,” Mr. Francisco wrote, “have overridden the president’s judgments on sensitive matters of national security and foreign relations, and severely restricted the ability of this and future presidents to protect the nation.”
The appeals court based its ruling on immigration statutes, not the Constitution’s prohibition of religious discrimination. But both sides urged the Supreme Court to consider both the statutory and constitutional questions if it agreed to hear the case.
Lawyers for the challengers told the justices that 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 one.
“The president has repeatedly explained that the two orders pursue the same aim,” the challengers wrote. Nine days before the September order was released, they wrote, “the president demanded a ‘larger, tougher and more specific’ ban, reminding the public that he remains committed to a ‘travel ban’ even if it is not ‘politically correct.’”
On the day the September order became public, the challengers added, “the president made clear that it was the harsher version of the travel ban, telling reporters, ‘The travel ban: the tougher, the better.’”
Mr. Francisco said discrimination had played no role in the September order. “The proclamation’s process and substance confirm that its purpose was to achieve national-security and foreign-policy goals, not to impose anti-Muslim bias,” Mr. Francisco wrote.
The Supreme Court, back at full strength after Mr. Trump’s appointment of Justice Neil M. Gorsuch to replace Justice Antonin Scalia, who died in 2016, already had an unusually large number of significant cases on its docket, including ones on voting rights, union power, digital privacy and a clash between claims of religious freedom and gay rights.