The outcome of Pennsylvania’s intensely fought Republican U.S. Senate primary remained uncertain as election officials continued to count mail ballots early Wednesday.

With 95% of the expected vote tabulated, the Associated Press had yet to call the contest, as celebrity surgeon Mehmet Oz and former hedge-fund executive David McCormick were separated by a razor-thin margin that could potentially send the race to a recount.

Unofficial results showed Mr. McCormick leading in votes cast by mail counted so far, while Mr. Oz was ahead in the Election Day vote.

Pennsylvania requires a recount in statewide races if the margin between the top two candidates is within 0.5 percentage points, a process that could take several days.

Army Reserve veteran and commentator Kathy Barnette, who had surged late in the contest, was in third place and too far behind to be a contender.

Since the state doesn’t allow officials to process mail ballots for tabulation ahead of Election Day, Pennsylvania is slower than some others to count votes.

President Trump had endorsed Mr. Oz, so his standing as a party kingmaker will either be enhanced or diminished based on the Pennsylvania outcome. All three of the top primary finishers portrayed themselves as strong supporters of the former president.

Even with the ballots of thousands of Pennsylvania voters left to count Wednesday, Mr. Trump wrote on his social-media platform that Mr. Oz should declare victory anyway and claimed without evidence that his chosen candidate could be cheated out of a win.

Both Mr. Oz and Mr. McCormick in speeches Tuesday evening projected confidence in their paths to victory once all votes were counted.

The winner of the GOP primary will face Democratic Lt. Gov. John Fetterman in November, a pivotal race in determining control of the Senate. Mr. Fetterman easily won the Democratic contest the same day he had a pacemaker implanted, after being knocked off the campaign trail by a stroke four days before the primary.

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