Washington — President Biden is set to travel to the battleground state of Wisconsin on Friday for a campaign rally, marking the start of a crucial weekend for his reelection bid as he seeks to assuage concerns about his fitness for a second term sparked by his startling debate performance just over one week ago.

In addition to the campaign event in Madison, Wisconsin, on Friday afternoon, Mr. Biden will tape an interview with ABC’s George Stephanopoulos, which the network said will air in full Friday night. The president will also head to Philadelphia for another campaign event on Sunday, capping the July 4 holiday weekend with a visit to a second battleground state.

The president’s appearances are coming under new scrutiny following his poor showing against former President Donald Trump, the presumptive Republican nominee, in the first general election debate on June 27. Mr. Biden blamed his performance on a busy travel schedule leading up to the face-off with Trump, saying during a campaign event Tuesday that he “almost fell asleep” on stage after making two trips to Europe in June.

In a pair of radio interviews that aired Thursday, Mr. Biden admitted he had a “bad debate” and that he “screwed up.”

Mr. Biden’s campaign and the White House sought to brush off concerns about his lackluster performance by insisting he had a cold and that the debate fiasco was simply a “bad night.” As part of efforts to quiet concerns about Mr. Biden and his age, he and Vice President Kamala Harris participated in a call with campaign staff on Wednesday, and they met with 20 Democratic governors at the White House later that evening. Mr. Biden also spoke with the Democratic leaders of the House and Senate, as well as other key allies on Capitol Hill.

The president has maintained the same message throughout the outreach, according to participants: he is in the race to defeat Trump and will not be pushed out.

“I learned from my father, when you get knocked down, just get back up, get back up,” Mr. Biden told “The Earl Ingram Show,” which airs in Wisconsin, in the radio interview Thursday. “And you know we’re going to win this election, we’re going to just beat Donald Trump.”

Amid the assurances, two House Democrats have openly called on Mr. Biden to withdraw from the presidential race: Reps. Lloyd Doggett of Texas and Raúl Grijalva of Arizona. Others, meanwhile, have publicly urged the president to take steps to prove to voters, elected Democrats and party donors that he is fit for a second term in the White House.