WASHINGTON — The Supreme Court on Monday allowed the third version of the Trump administration’s travel ban to go into effect while legal challenges against it continue. The decision was a victory for the administration after its mixed success before the court over the summer, when justices considered and eventually dismissed disputes over the second version.

The court’s brief, unsigned order on Monday urged appeals courts to move swiftly to determine whether the latest ban was lawful. Justices Ruth Bader Ginsburg and Sonia Sotomayor said they would have denied the administration’s request to allow the latest ban to go into effect.

The third and newest version of the ban, issued by President Trump in a proclamation in September, imposed restrictions on citizens of Chad, Iran, Libya, North Korea, Somalia, Syria, Venezuela and Yemen. In a pair of filings in the Supreme Court, Solicitor General Noel J. Francisco said Mr. Trump had acted under his broad constitutional and statutory to control immigration.

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Mr. Francisco wrote that the process leading to the September proclamation was more deliberate than those that had led to earlier bans, issued in January and March. Those earlier orders were temporary measures, he wrote, while the proclamation was the product of extensive study and deliberation.

Lawyers with the American Civil Liberties Union, which represents people and groups challenging the ban, told the justices that little had changed. “The proclamation is the third order the president has signed this year banning more than 100 million individuals from Muslim-majority nations from coming to the United States,” they wrote.

In October, federal judges in Maryland and Hawaii blocked major parts of the latest ban while legal challenges proceed.

“A nationality-based travel ban against eight nations consisting of over 150 million people is unprecedented,” wrote Judge Theodore D. Chuang, of the Federal District Court in Maryland. Citing statements from Mr. Trump, some made as a presidential candidate and some more recent, Judge Chuang found that the new proclamation was tainted by religious animus and most likely violated the Constitution’s prohibition of government establishment of religion.

Similarly, Judge Derrick K. Watson of the Federal District Court in Honolulu found that the September proclamation “suffers from precisely the same maladies as its predecessor,” adding that it “plainly discriminates based on nationality” in violation of federal law “and the founding principles of this nation.”

The administration has appealed both decisions to federal appeals courts in Seattle and Richmond, Va. Arguments in those appeals are scheduled for this week.

Judge Chuang limited his injunction to exclude people without “a credible claim of a bona fide relationship with a person or entity in the United States,” quoting from a Supreme Court order issued in June concerning the second travel ban. Judge Watson did not impose such a limitation, but an appeals court modified his injunction, also quoting the Supreme Court’s language.

Lawyers for Hawaii, which is challenging the ban, told the justices that there was no reason to make changes now.

“Less than six months ago, this court considered and rejected a stay request indistinguishable from the one the government now presses,” they wrote. “But the justification for that dramatic relief has only weakened. In place of a temporary ban on entry, the president has imposed an indefinite one, deepening and prolonging the harms a stay would inflict.”

Mr. Francisco asked the justices allow every part of the third ban to go into effect. The second version of the travel ban, he wrote, “involved temporary procedures before the review was conducted and in the absence of a presidential determination concerning the adequacy of foreign governments’ information-sharing and identity-management practices.”

“Now that the review has been completed and identified ongoing deficiencies in the information needed to assess nationals of particular countries,” he wrote, “additional restrictions are needed.”