But under pressure to salvage the caucuses from a humiliating logistical debacle, Iowa Democratic leaders decided to go ahead with releasing numbers from a majority of precincts without waiting for the counting process to be completed.

The halting and hectic process in Iowa was an unsightly spectacle for the Democratic Party at the start of its presidential nominating process, offering President Trump an easy target for gloating and ridicule and raising serious questions about whether Iowa would be allowed to retain its first-in-the-nation status in future elections.

Troy Price, the chairman of the Iowa Democratic Party, appeared downcast on Tuesday as he described the process as “unacceptable” in remarks to reporters. “As chair of the party, I apologize deeply for this,” he said.

Mr. Price repeatedly stressed that the data was accurate and said the security of the returns was his “paramount concern.”

The returns posted on Tuesday largely mirrored the scenario that the leading presidential campaigns detected during the caucuses, gathering precinct-level information on their own and in some cases releasing it to the media to make up for the void of hard results.

Should the rest of the Iowa results mostly mirror the data published on Tuesday, it could represent a significant embarrassment for Mr. Biden, who entered the race as a front-runner last spring but has struggled mightily in recent months to compete with fresher-faced and more liberal rivals in both Iowa and New Hampshire. For a period in January, his campaign had grown hopeful that he had a chance of winning Iowa and establishing early dominance, but by caucus night that seemed a remote prospect.

Mr. Biden is aiming to retake control of the race later in February, when the competition moves to Nevada and South Carolina, two far more diverse states long seen as friendly to his candidacy. But first he may have to explain his Iowa slump to the political donors whose support he needs to compete in the larger primary states that vote at the beginning of March.