Dr. Oz was leading Mr. McCormick by 902 votes as of Wednesday, according to Leigh M. Chapman, the state’s acting secretary of the commonwealth, who said that all 67 of Pennsylvania’s counties had reported unofficial tallies to the state.

The recount could lead to a series of lawsuits and challenges in the marquee primary, one that could ultimately determine control of the closely divided Senate. That legal wrangling has already begun: On Monday, Mr. McCormick filed a lawsuit demanding that undated mail-in ballots should be counted.

A victory for Mr. McCormick — a West Point graduate and the former chief executive of Bridgewater Associates, the world’s largest hedge fund — would be a significant rebuke to Mr. Trump, who supported Dr. Oz and campaigned for him in Pennsylvania. The seat will be open after Senator Patrick J. Toomey, a Republican, steps down this year…

State elections officials acknowledged that the recount could be a slog, one that they said could cost taxpayers in Pennsylvania more than $1 million.