PHILADELPHIA — At a rally in Erie last month, John Fetterman said he turned down living in the “lieutenant governor governor.” He meant the “lieutenant governor’s mansion,” trying to draw a distinction between himself and his opponent, a celebrity with several multimillion-dollar homes.

In Pittsburgh a week later, Mr. Fetterman jumbled up his point about good-paying jobs. “What is wrong with demanding for an easy, safe, kind of their income, a path to a safe place for them to win? Excuse me, to work?” he said.

As Mr. Fetterman has returned to the trail, giving candid speeches without notes, he’s been upfront about the lingering speech impacts of his May stroke, insisting his physical and mental health are good, while his opponent, Mehmet Oz, challenges his ability to serve.

“My health now is robust. I’m able to live a normal life,” Mr. Fetterman said in his first nationally televised interview since his stroke on MSNBC. “Driving, going to the grocery store ... it’s just that every now and then, I’m going to miss a word or mush two words together.”

Mr. Fetterman and his Senate campaign have said it’s called auditory processing, an effect of his May 13 stroke, along with some word retrieval issues, which they expect to continue to improve. In brief speeches he’s given on the trail, it’s noticeable but not an overwhelming distraction. His crowds, typically supporters, enthusiastically respond to him, and plenty of people have speech problems that don’t indicate cognitive impairment.

As clips of Mr. Fetterman’s verbal fumbles have circulated, Mr. Oz, a cardiothoracic surgeon who trails slightly in most polls, has amped up pressure on Mr. Fetterman to debate. Mr. Fetterman said on Wednesday that he will debate Mr. Oz sometime in mid- to late October. His campaign has stressed that he is fully capable of serving as a U.S. senator.