ATLANTA — A raspy President Joe Biden delivered rambling answers Thursday in the opening moments of his debate with his Republican rival, Donald Trump, who countered Biden’s criticism with energy and at times by leaning into falsehoods about the economy and illegal immigration.

The debate came at a pivotal juncture in their unpopular presidential rematch, as Biden, the 81-year-old Democratic incumbent, entered the debate with the chance to reassure voters that he’s capable of guiding the U.S. through a host of challenges as he moved to sharpen the choice voters will face in November. Trump, 78, had the opening to try to move past his felony conviction in New York and convince an audience of tens of millions that he is temperamentally suited to return to the Oval Office.