McCormick said he had called Oz to concede.
"It's now clear to me with the recount now largely complete that we have a nominee," McCormick said at a campaign party at a Pittsburgh hotel. "Tonight is really about all us coming together."
Before the recount, Oz led McCormick by 972 votes, or 0.07 percentage points, out of 1.34 million votes counted in the May 17 primary. The Associated Press has not declared a winner in the race because an automatic recount is underway.
Friday's development sets up a general election between Oz, who was endorsed by former President Donald Trump, and Democrat John Fetterman in what is expected to be one of the nation's premier Senate contests. The race could help determine control of the closely divided chamber.
Fetterman, the state's lieutenant governor, acknowledged earlier Friday in a statement that he nearly died when he suffered a stroke just days before his primary. He said he had ignored warning signs for years and a doctor's advice to take blood thinners.
Oz, who is best known as the host of daytime TV's "The Dr. Oz Show," had to overcome millions of dollars in attack ads and misgivings among hard-line Trump backers about his conservative credentials on guns, abortion, transgender rights and other core Republican issues.
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The 61-year-old Oz leaned on Trump's endorsement as proof of his conservative bona fides, while Trump attacked Oz's rivals and maintained that Oz has the best chance of winning in November in the presidential battleground state.
Rivals made Oz's dual citizenship in Turkey an issue in the race. If elected, Oz would be the nation's first Muslim senator.
Born in the United States, Oz served in Turkey's military and voted in its 2018 election. Oz said he would renounce his Turkish citizenship if he won the November election, and he accused McCormick of making "bigoted" attacks.
Oz and McCormick blanketed state airwaves with political ads for months, spending millions of their own money. Virtually unknown four months ago, McCormick had to introduce himself to voters, and he mined Oz's long record as a public figure for material in attack ads. He got help from a super PAC supporting him that spent $20 million.
Like McCormick, Oz moved from out of state to run in Pennsylvania.
Oz, a Harvard graduate, New York Times bestselling author and self-styled wellness advocate, lived for the past couple of decades in a mansion in Cliffside Park, New Jersey, above the Hudson River overlooking Manhattan - drawing accusations of being a carpetbagger and political tourist.
The celebrity heart surgeon stressed his connections to Pennsylvania, saying he grew up just over the state border in Delaware, went to medical school in Philadelphia and married a Pennsylvania native.