McCormick sues to count undated mail-in ballots, trailing Oz in Pennsylvania Senate race.

“Every Republican primary vote should be counted, including the votes of Pennsylvania’s active-duty military members who risk their lives to defend our constitutional right to vote,” Jess Szymanski, a spokeswoman for Mr. McCormick’s campaign, said in an email on Monday night.

Dr. Oz on Monday posted on Twitter a statement by his campaign manager, Casey Contres, criticizing Mr. McCormick’s move, saying that while he had been a formidable opponent, “he is likely going to come up short.”

“Unfortunately, the McCormick legal team is following the Democrats’ playbook, a tactic that could have long-term harmful consequences for elections in the Commonwealth of Pennsylvania,” Mr. Contres said. “Dr. Mehmet Oz continues to respectfully allow Pennsylvania’s vote-counting process to take place and puts his faith in the Republican voters who we believe have chosen him as their nominee.”

Mr. McCormick’s argument that undated mail-in ballots were still valid received a rocky reception on Monday from the Pennsylvania Republican Party. And the Republican National Committee and the Pennsylvania G.O.P. are planning to formally intervene against Mr. McCormick in the suit he filed, two Republicans said on Monday.

“We absolutely object to the counting of undated mail-in ballots,” the party said on Twitter. “Pennsylvania law and our courts have been very clear that undated ballots are not to be counted. We have worked hard towards restoring confidence in our elections, and we call upon everyone to respect, uphold and follow the clear law on this issue.”

The party’s statement echoed comments that Ronna McDaniel, the chairwoman of the Republican National Committee, made on Fox News on Sunday.

“Well,” Ms. McDaniel said, “the Pennsylvania Supreme Court ruled this year, and the R.N.C. very much supports, that ballots should not be counted without a date. I think that’s the law in Pennsylvania. I think that should be followed, and we certainly do not think that ballots without dates should be counted because how do you know when they came in? I think that is common sense, and that is definitely where the R.N.C. and the G.O.P. is.”

Maggie Haberman contributed reporting.