President Trump and his former secretary of state, Mike Pompeo, are appearing on opposing campaign dais Friday in Pennsylvania, a state shaping up to be one of the next bellwethers of the former president’s grip on the GOP.

Mr. Trump was scheduled to appear at a rally in Greensburg with Mehmet Oz, the Turkish-American television personality in the middle of a tight Republican primary contest to take over the seat of Senator Toomey, who is retiring.

Mr. Trump endorsed Dr. Oz last month and will appear at the rally along with J.D. Vance, a Trump endorsee who prevailed over his Republican primary challengers on Tuesday in Ohio, and a host of other MAGA-world celebrities such as the MyPillow CEO, Mike Lindell, and a right-wing pundit, Dinesh D’Souza.

The Pennsylvania Senate seat is widely considered to be a toss-up in the November midterm vote and has the potential to decide which party controls the U.S. Senate for the second half of President Biden’s first term. The vote to decide the Republican contender in the fall is May 17.  

One of Dr. Oz’s opponents, David McCormick, a former hedge fund CEO and Treasury Department official, convened a press briefing with Mr. Pompeo Friday morning at which the former Trump acolyte questioned Dr. Oz’s loyalties and said his candidacy creates “national security concerns.”

“Maybe it’s all innocent, maybe it’s all straight up, but we and the people of Pennsylvania and the Americans who he will be representing as one of the 100 members of the United States Senate voting on important national security matters need to understand the scope and depth of his relationship with the Turkish government,” Mr. Pompeo said at the briefing.

Mr. Pompeo is widely considered to be contemplating his own run for the presidency, making regular trips to Iowa and New Hampshire in recent months and undergoing a jaw-dropping physical makeover that saw him shed 90 pounds since the Trump presidency.

Dr. Oz has come under fire for his dual-national status as a citizen of both the United States and Turkey. To maintain that status, he served in the Turkish army and has close business and political ties to the country and its autocratic leader, Recep Tayyip Erdogan.

This week, reports surfaced that Dr. Oz voted in the most recent presidential election in Turkey in 2018. Photos of him casting his ballot emerged after Dr. Oz professed to be uninvolved in Turkish politics “in any capacity.”

“We criticize American candidates all the time because they didn’t vote,” Mr. Pompeo, who also served as head of the Central Intelligence Agency during the Trump presidency, said. “This is different from that. Not only did he not engage in the American [process] but he engaged in the Turkish political process. That raises in my mind a lot of judgments about his priority.”

The latest polling in the race has the two Republican candidates essentially tied for the top spot and a third contender — Kathy Barnette — not far behind them.

A Franklin & Marshall College poll released Thursday put Dr. Oz at 18 percent, Mr. McCormick at 16 percent, and Ms. Barnette at 12 percent. More than a third of respondents to the poll, however, said they were undecided.

A campaign official for Dr. Oz called Mr. Pompeo’s characterizations of the candidate “pathetic and xenophobic.”

“Now that he lost President Trump’s endorsement, he’s resorted to sad and desperate attacks that are no different than the tropes used against Catholics and Jews,” the campaign’s communications director, Brittany Yanick, said in a statement.

“Dr. Oz has already said when elected to the Senate he would renounce his citizenship,” she added. “There is no security issue whatsoever, and David McCormick knows that Dr. Oz has maintained his dual citizenship to make it easier to help care for his mother who has Alzheimer’s and lives there.”