President Biden on Friday dismissed concerns about his age, his mental acuity and polls showing him losing his re-election bid, saying in a prime-time interview that his sharpness is tested every day while he is “running the world.” He vowed to drop out only if “the Lord Almighty” told him to.

During a 22-minute interview with ABC’s George Stephanopoulos, which aired unedited, Mr. Biden, 81, said there was no need for him to submit to neurological or cognitive testing. He said he simply did not believe the polls showing him losing. And asked how he would feel if former President Donald J. Trump were elected in November, he brushed off the question.

“I’ll feel as long as I gave it my all and I did the goodest job as I know I can do, that’s what this is about,” Mr. Biden said in an interview that was intended to assuage growing concerns about his age following last Thursday’s debate. But with him speaking in a hoarse voice and remaining defiant throughout, there was little indication that the interview would do much to stanch the bleeding during the deepest crisis of a long political career.

Again and again, Mr. Biden told Mr. Stephanopoulos that voters should consider his accomplishments in office.

“Who’s going to be able to hold NATO together like me?” he said. “Who’s going to be able to be in a position where I’m able to keep the Pacific Basin in a position where, at least we’re checkmating China now? Who’s going to do that? Who has that reach?”

Mr. Biden repeatedly waved off “hypothetical” questions about whether he would step aside for another Democrat if people he respects say that he can’t win in the fall.