Former Vice President Dick Cheney had a defibrillator implanted in 2001. He finished two terms in the White House, including a hard-fought re-election campaign in 2004.

“Doctors have told me I need to continue to rest, eat healthy, exercise, and focus on my recovery, and that’s exactly what I’m doing,” Mr. Fetterman said. “It will take some more time to get back on the campaign trail like I was in the lead-up to the primary. It’s frustrating — all the more so because this is my own fault — but bear with me, I need a little more time. I’m not quite back to 100 percent yet, but I’m getting closer every day.”

When he does return to the campaign trail, it appears his Republican opponent will be Dr. Mehmet Oz, the celebrity television physician. With a statewide recount still underway on Friday in the Republican Senate primary and no official race call, David McCormick conceded the race to Dr. Oz.

Ed Rendell, a Democratic former governor of the state and a former chairman of the Democratic National Committee, said in an interview on Friday that he had no qualms about Mr. Fetterman’s fitness to serve. He downplayed how much Mr. Fetterman’s health would weigh on the minds of voters, saying that he did not think it would be an issue.

“When I was governor, the Republicans used to say I was one cheese steak away from having a heart attack, and I never did,” said Mr. Rendell.

Nancy Patton Mills, the chairwoman of the Pennsylvania Democrats, did not immediately respond to a request for comment on Friday. The Democratic Senatorial Campaign Committee did not immediately comment on Friday.

Mr. Fetterman has been off the campaign trail since his stroke and has occasionally released brief videos since then. In a sign that Mr. Fetterman was moving back toward some political engagement, Senator Bob Casey, Democrat of Pennsylvania, wrote on Twitter that he’d had a “virtual double date” with Mr. Fetterman and his wife, Gisele Barreto Fetterman, earlier Friday afternoon.

“Looking forward to many more on the campaign trail this summer!” Mr. Casey wrote.

Gina Kolata and Neil Vigdor contributed reporting.