Mr. Buttigieg, however, still enjoyed a slight lead according to the Iowa Democrats’ complex formula for allocating delegates, the traditional metric for determining a winner. At a veterans-themed event in Merrimack, N.H., on Thursday, he ignored the tightening results, citing the “extraordinary validation of this campaign’s vision that we had in Iowa on Monday.”

But even as the two candidates trumpeted their performance, analyses by political scientists and The New York Times’s Upshot section indicated inconsistencies in the results Iowa has provided. The Times’s analysis found the Iowa returns riddled with problems, with over 100 precincts reporting results that were internally inconsistent, missing data or not possible under the complex rules of the Iowa caucuses.

There was no indication that the inconsistencies affected the order of the race or were a result of an intentional effort to rig the outcome, but they added to the questions raised about results that have been mired in chaos for three days.

Iowa’s caucuses suffered from cascading calamities. Volunteer precinct leaders either refused to download a new smartphone app designed for reporting caucus results or found it too cumbersome to use. Those who tried to phone in results found the phone lines jammed. And when the state party did receive results from its 1,758 precincts, the calculations to determine how many delegates each candidate won turned out to be incorrect in as many as 20 percent of precincts.

Mr. Sanders seized on the trouble to excoriate party officials.

“What has happened with the Iowa Democratic Party is an outrage,” he said at his news conference, “that they were that unprepared, that they put forth such a complicated process, relying on untested technology.”

The recanvass requested by Mr. Perez would involve examining work sheets from caucus precincts across the state and 87 satellite caucus precincts in Iowa, other states and overseas. But Mr. Perez has no authority to order Iowa Democrats to recanvass their results. And in an interview later in the day on MSNBC, he said had not been calling for a recanvass statewide — only in precincts where irregularities had been reported.

More troubling to Democratic strategists and elected officials was the growing strain between Mr. Perez, who has struggled to hold his divided party together, and Mr. Sanders’s campaign.