WASHINGTON — The Supreme Court announced on Monday that it would not hear an appeal from Pennsylvania Republicans who sought to disqualify mailed ballots in the 2020 presidential election that arrived after Election Day.

The court’s brief order gave no reasons for turning down the case, which as a practical matter marked the end of Supreme Court litigation over the election. Justices Clarence Thomas, Samuel A. Alito Jr. and Neil M. Gorsuch dissented, saying the court should have used it to provide guidance in future elections.

The dissenting justices acknowledged that the number of ballots at issue in the case was too small to affect President Biden’s victory in the state. But the legal question the case presented — about the power of state courts to revise election laws — was, they said, a significant one that should be resolved without the pressure of an impending election.

The Pennsylvania Supreme Court ruled in September that ballots sent before Election Day could be counted if they arrived up to three days after. On two occasions before the election, the U.S. Supreme Court declined to intervene in the case, though several justices expressed doubts about the state court’s power to override the State Legislature, which had set an Election Day deadline for receiving mailed ballots.

On Monday, Justice Thomas wrote that the time was now right to take up the case.

“At first blush,” he wrote, “it may seem reasonable to address this question when it next arises. After all, the 2020 election is now over, and the Pennsylvania Supreme Court’s decision was not outcome determinative for any federal election. But whatever force that argument has in other contexts, it fails in the context of elections.”

“Because the judicial system is not well suited to address these kinds of questions in the short time period available immediately after an election,” Justice Thomas wrote, “we ought to use available cases outside that truncated context to address these admittedly important questions.”

In a separate dissent, Justice Alito, joined by Justice Gorsuch, agreed that “our review at this time would be greatly beneficial.”

“A decision in these cases would not have any implications regarding the 2020 election,” Justice Alito wrote. “But a decision would provide invaluable guidance for future elections.”

On Oct. 19, before Justice Amy Coney Barrett joined the court, the justices deadlocked, 4 to 4, on an emergency application in the case. Justices Thomas, Alito, Gorsuch and Brett M. Kavanaugh said they would have granted a stay blocking the Pennsylvania Supreme Court’s decision. On the other side were Chief Justice John G. Roberts Jr. and the court’s three-member liberal wing: Justices Stephen G. Breyer, Sonia Sotomayor and Elena Kagan.

Later that month, the justices refused a plea from Republicans in the state to fast-track a decision on whether the Pennsylvania Supreme Court had acted lawfully.

In a statement issued at the time, Justice Alito, joined by Justices Thomas and Gorsuch, criticized the court’s treatment of the matter, which he said had “needlessly created conditions that could lead to serious postelection problems.”

“The Supreme Court of Pennsylvania has issued a decree that squarely alters an important statutory provision enacted by the Pennsylvania Legislature pursuant to its authority under the Constitution of the United States to make rules governing the conduct of elections for federal office,” Justice Alito wrote, adding that he regretted that the election would be “conducted under a cloud.”

“It would be highly desirable to issue a ruling on the constitutionality of the State Supreme Court’s decision before the election,” Justice Alito wrote. “That question has national importance, and there is a strong likelihood that the State Supreme Court decision violates the federal Constitution.”

But there was not enough time, he wrote. Still, Justice Alito left little doubt about where he stood on the question in the case.

“The provisions of the federal Constitution conferring on state legislatures, not state courts, the authority to make rules governing federal elections would be meaningless,” he wrote, “if a state court could override the rules adopted by the legislature simply by claiming that a state constitutional provision gave the courts the authority to make whatever rules it thought appropriate for the conduct of a fair election.”

Even after the election, Pennsylvania Republicans continued to seek Supreme Court review in the case, Republican Party of Pennsylvania v. Boockvar, No. 20-542, saying the justices should address the issue it presented in an orderly way.

“By resolving the important and recurring questions now, the court can provide desperately needed guidance to state legislatures and courts across the country outside the context of a hotly disputed election and before the next election,” their brief said. “The alternative is for the court to leave legislatures and courts with a lack of advance guidance and clarity regarding the controlling law — only to be drawn into answering these questions in future after-the-fact litigation over a contested election, with the accompanying time pressures and perceptions of partisan interest.”

On Monday, Justice Thomas wrote that the court had missed an opportunity.

“One wonders what this court waits for,” he wrote. “We failed to settle this dispute before the election, and thus provide clear rules. Now we again fail to provide clear rules for future elections.”

“The decision to leave election law hidden beneath a shroud of doubt is baffling,” Justice Thomas wrote. “By doing nothing, we invite further confusion and erosion of voter confidence. Our fellow citizens deserve better and expect more of us.”