Case’s legal path forward may be complicated by current 4-4 ideological split on the Supreme Court

WASHINGTON—A federal appeals court, based in San Francisco, is set to rule as soon as this week on President Donald Trump’s executive order on immigration in a decision that may have more influence—and last longer—than usual because of the longstanding vacant seat on the U.S. Supreme Court.

The Ninth U.S. Circuit Court of Appeals early Sunday morning denied a request from the Justice Department to immediately restore the executive order after U.S. District Judge James Robart, a federal judge in Seattle, late on Friday issued a restraining order against enforcement of the travel ban.

The ban suspended entry to the U.S. for visitors from seven predominantly Muslim countries for at least 90 days, saying such action was needed to keep terrorists from entering the U.S. The order also sought to freeze the entire U.S. refugee program for four months.

Over the weekend, Mr. Trump repeatedly criticized Judge Robart’s ruling. “Just cannot believe a judge would put our country in such peril,” he posted Sunday afternoon on Twitter. “If something happens blame him and court system. People pouring in. Bad!

The appeals court in its order early Sunday asked for further legal briefings on the issue, the last of them due Monday afternoon. The case was brought by the state of Washington and was joined by the state of Minnesota.

The earliest the appeals court could reach a decision on whether to reinstate the ban during the ongoing court case would be late Monday.

Either side could appeal any action by the appeals court, asking the Supreme Court to intervene. But that may prolong the legal limbo, potentially for months.

Given the current 4-4 split on the Supreme Court between liberal-leaning and conservative-leaning justices, it is possible that the losing side at the Ninth Circuit won’t be able to muster the support needed among the justices for high-court intervention. An emergency stay of the lower court ruling by the Supreme Court would require agreement from five justices. A Supreme Court tie vote would leave the Ninth Circuit decision in place.

The Ninth Circuit has long been regarded as perhaps the nation’s most prominent left-leaning appeals court, though such leanings aren’t necessarily predictive of how three-judge panels will rule on specific issues. A large majority of judges on the court have been appointed by Democratic presidents.

The vacancy on the high court remains open because Republicans declined to act on U.S. Circuit Judge Merrick Garland’s nomination by former President Barack Obama to succeed the late Justice Antonin Scalia, saying they wanted to allow voters to weigh in on the court’s direction by electing the next president.

The justices have found ways to come together in a range of cases, but even with Chief Justice John Roberts’s push for consensus, the eight-member court has found itself at loggerheads in some ideologically divisive cases. And those tie votes have left some areas of the law unsettled, including in a major case last year involving Obama administration efforts to assist illegal immigrants.

It isn’t yet clear if Mr. Trump’s immigration order would produce those kinds of divisions, and lower court judges appointed by both liberal and conservative presidents have ruled against the administration so far. But if there were gridlock at the high court, the ruling from the Ninth Circuit could be the final word on what legal rules are in place in the near term while a flurry of court challenges unfold.

Mr. Trump last week nominated Judge Neil Gorsuch as his nominee to fill the vacant seat, though his nomination process may become a prolonged fight given that some Democratic senators feel they were unfairly deprived of consideration for Judge Garland.

The eight current Supreme Court justices don’t automatically split into ideological camps and broad agreement among them is possible. The previous immigration split, however, highlights potential court tensions. The justices deadlocked last June on the Obama administration’s plan to defer deportations and allow work authorization for millions of illegal immigrants.

At some point months down the road, a nine-judge Supreme Court may decide to answer the overarching legal question of how much authority a president has to decide who does and doesn’t enter the U.S.

Mr. Trump, meanwhile, ramped up his criticism Sunday of the legal wrangling over the ban, saying the courts should be blamed if there is a terrorist attack.

For now, immigration agents aren’t enforcing Mr. Trump’s Jan. 27 order. A small number of people from the targeted countries in the ban began to clear customs this weekend without incident, immigration attorneys said.

On Saturday, also on Twitter, Mr. Trump had referred to Judge Robart as “this so-called judge,” an attack that made some Republicans uneasy. “I think it’s best not to single out judges for criticism,’’ Senate Majority Leader Mitch McConnell (R., Ky.) told CNN on Sunday.

Mr. Trump’s comments this weekend aren’t the first time he has publicly attacked a federal judge. During the presidential campaign, he criticized a judge overseeing civil fraud lawsuits against Trump University, claiming Judge Gonzalo Curiel had “an absolute conflict’’ in presiding over the litigation because he was of Mexican heritage. The judge was born in the U.S.

After the election, Mr. Trump reached a $25 million settlement to end the litigation. He didn’t admit wrongdoing.

Over the weekend, government lawyers filed court papers arguing that because the executive order was issued out of a concern for national security, it is wrong and potentially dangerous for a court to review such judgments.

“Judicial second-guessing of the president’s national security determination in itself imposes substantial harm on the federal government and the nation at large,’’ Justice Department lawyers wrote in legal papers defending the executive order.

Noah Purcell, a lawyer for the state of Washington, which had filed the suit, criticized that reasoning at Friday’s court hearing.

“They’re basically saying that you can’t review anything about what the president does or says, as long as he says it’s for national security reasons. And that just can’t be the law.’’

Mr. Trump’s executive order, which suspended entry to the U.S. of visitors from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen, indefinitely barred Syrians from entering as refugees. It cut the number of refugees the U.S. will accept in fiscal 2017 to 50,000—less than half the number former President Barack Obama called for this year.

The order caused confusion and confrontations at major U.S. airports, as some travelers were detained for many hours or sent away, and protesters gathered to denounce the new rules.

Late Friday, Judge Robart issued the restraining order against enforcement of the travel ban. About 24 hours later, the Justice Department filed papers appealing that order.

Two appeals-court judges, both nominated by Democratic presidents, rejected a request to immediately stop the order, but made clear they plan to get more information before making a decision.

Judge Robart wrote that he was granting the order because the plaintiffs, which included the state of Washington, were likely to win on their constitutional claims.

Not halting the president’s order would cause the plaintiffs “irreparable injury,” wrote Judge Robart, who was appointed to the federal bench by President George W. Bush.

In response to Judge Robart’s order, the U.S. Departments of State and Homeland Security said Saturday they had stopped enforcing Mr. Trump’s executive order. If the appeals court rules for Mr. Trump’s administration, they likely would resume enforcing it.

Mr. Trump’s executive order already had been hit with dozens of lawsuits as individuals, civil-rights groups and state officials sought to strike it down on constitutional or other legal grounds.