Supreme Court action on undated ballots in a Pennsylvania race is watched closely by Oz and McCormick.

In a move that could reverberate throughout Pennsylvania’s elections, including its undecided Republican Senate primary between Dr. Mehmet Oz and David McCormick, the U.S. Supreme Court on Tuesday paused the counting of some mail-in ballots in a county judicial race.

Justice Samuel A. Alito Jr. granted an “administrative stay” that temporarily blocked elections officials in Lehigh County, Pa., from accepting mail-in ballots without handwritten dates, which is required by a state law.

The developments in the Lehigh County case have been intensely followed by Mr. McCormick and Dr. Oz, who are separated by fewer than 1,000 votes with a statewide recount underway in their race, which could ultimately determine control of the divided Senate.

Undated ballots are also at issue in that contest: Mr. McCormick filed a separate lawsuit last week seeking to have such ballots counted. His case is pending before the Commonwealth Court of Pennsylvania.

The provisional order from the Supreme Court came after a Republican judicial candidate in Lehigh County submitted an emergency application on Friday, asking Justice Alito to halt a recent ruling by the U.S. Court of Appeals for the Third Circuit that allowed undated ballots to be counted.

Mr. McCormick, a former hedge fund executive who was trailing by less than 0.1 percent against Dr. Oz, the Trump-backed celebrity physician, had placed an emphasis on the Lehigh County ruling in his lawsuit. Oral arguments in the McCormick lawsuit took place on Tuesday, hours before Justice Alito issued the administrative stay.

Jess Szymanski, a spokeswoman for Mr. McCormick’s campaign, said that Justice Alito’s temporary stay did not have a bearing on the proceedings in Mr. McCormick’s lawsuit.

Mr. McCormick wants Pennsylvania’s 67 counties to accept mail-in ballots from voters who turned them in by the May 17 deadline but did not write the date on the outer return envelopes.

That step is required by a state law, one that Republicans have fought to preserve.

In the Lehigh County case, a unanimous three-judge panel of the U.S. Court of Appeals for the Third Circuit, in Philadelphia, ruled that the handwritten date requirement ran afoul of a provision of the federal Civil Rights Act of 1964. The provision prohibits government officials from denying the right to vote “because of an error or omission” if it “is not material in determining whether such individual is qualified under state law to vote.”

“The Third Circuit’s opinion remains the persuasive authority on the federal Civil Rights Act issue presented to the Commonwealth Court,” Ms. Syzmanski said. “The Commonwealth Court has every right to side with Republican voters throughout the commonwealth who cast a timely ballot on grounds rooted in the Pennsylvania Constitution.”

The campaign of Dr. Oz, who proclaimed himself the presumptive Republican nominee in a campaign video on Friday, did not immediately respond to a request for comment on Wednesday. Dr. Oz’s campaign had filed a friend of the court brief with the Supreme Court supporting the emergency request for a stay.

“Dr. Oz’s principal competitor, David McCormick, has invoked the panel’s judgment in a Hail Mary effort to overturn the apparent result of that election,” Dr. Oz’s lawyers wrote in the brief. “In particular, Mr. McCormick has asked the Pennsylvania courts to change the rules of the primary election after voting has been completed.” The brief argued that ballots without a handwritten date are “invalid under Pennsylvania law.”

Justice Alito on Tuesday agreed to issue the administrative stay to give the Supreme Court time to consider the lawfulness of requiring voters who use such ballots to enter a date next to their signatures on the outer envelope.

Voters challenging the requirement said that it served no purpose.

It was undisputed that the undated ballots at issue in the case were received by Election Day and that the local elections board had accepted ballots with incorrect dates, including birth dates.

Justice Alito’s stay was provisional, and the full Supreme Court may rule on whether to stay the Third Circuit’s decision in the coming days.