Earlier this month, when Senator Bernie Sanders said he would not challenge President Biden in 2024, Mr. Biden was so relieved he invited his former rival to dinner at the White House the next night.

Mr. Biden has been eager for signs of loyalty — and they have been few and far between. Facing intensifying skepticism about his capacity to run for re-election when he will be nearly 82, the president and his top aides have been stung by the questions about his plans, irritated at what they see as a lack of respect from their party and the press, and determined to tamp down suggestions that he’s effectively a lame duck a year and a half into his administration.

Mr. Biden isn’t just intending to run, his aides argue, but he’s also laying the groundwork by building resources at the Democratic National Committee, restocking his operation in battleground states and looking to use his influence to shape the nomination process in his favor.

This account of Mr. Biden’s preparation for re-election and his building frustration with his party’s doubt is based on interviews with numerous people who talk regularly to the president.