WASHINGTON — A sharply divided Supreme Court on Tuesday allowed Texas to continue enforcing abortion restrictions that opponents say have led more than a third of the state’s clinics to stop providing abortions.

The justices voted 5-4 to leave in effect a provision requiring doctors who perform abortions in clinics to have admitting privileges at a nearby hospital.

The court’s conservative majority refused the plea of Planned Parenthood and several Texas abortion clinics to overturn a preliminary federal appeals court ruling that allowed the provision to take effect.

The four liberal justices dissented.

The case remains on appeal to the 5th U.S. Circuit Court of Appeals in New Orleans. That court is expected to hear arguments in January, and the law will remain in effect at least until then. Justice Stephen Breyer, writing for the liberal justices, said he expects the issue to return to the Supreme Court once the appeals court issues its final ruling.

The Texas Legislature approved the requirement for admitting privileges in July.

In late October, days before the provision was to take effect, a trial judge blocked it, saying it probably is unconstitutional because it puts a “substantial obstacle” in front of a woman wanting an abortion.

But a three-judge appellate panel moved quickly to overrule the judge. The appeals court said the law was in line with Supreme Court rulings that have allowed for abortion restrictions so long as they do not impose an “undue burden” on a woman’s ability to obtain an abortion. Writing for the appeals court, Judge Priscilla Owen noted that the Texas law would not end the procedure, only force women to drive a greater distance to obtain one.

Justice Antonin Scalia, writing in support of the high court order Tuesday, said the clinics could not overcome a heavy legal burden against overruling the appeals court. The justices may not do so “unless that court clearly and demonstrably erred,” Scalia said in an opinion that was joined by Justices Samuel Alito and Clarence Thomas.

Chief Justice John Roberts and Justice Anthony Kennedy did not write separately or join any opinion Tuesday, but because it takes five votes to overturn the appellate ruling, it is clear that they voted with their conservative colleagues.

Planned Parenthood and several Texas abortion clinics said in their lawsuit to stop the measure that it would force more than a third of clinics in the state to stop providing abortions.