Republican candidates and conservative media organizations seized on reports of voting issues in Arizona on Tuesday to re-up their case that the state’s elections are broken and in need of reform, even as state and county officials said the complaints were exaggerated.

“We’ve got irregularities all over the state,” Mark Finchem, who won the Republican nomination for secretary of state in Arizona, said before his victory was announced.

Gateway Pundit, a conservative website that breathlessly covered the election rumors on Tuesday, wrote that Arizona’s largest counties were apparently “rife with serious irregularities that have been occurring all day long, sparking even more concern for election integrity.”

There is no evidence of any widespread fraud in Tuesday’s election. But the concerns raised were bolstered by a number of problems in Pinal County, the state’s third-most populated county, located between Phoenix and Tucson. More than 63,000 ballots were mailed with the wrong local races on them, requiring new ballots to be issued. On election night, at least 20 of 95 precincts in Pinal County were running low on ballots or ran out entirely.

Sophia Solis, the deputy communications director of Arizona’s secretary of state, said voters could still cast a ballot at those precincts using voting machines that are typically used by disabled voters.

“We did not hear of any widespread problems,” Ms. Solis said, adding that “one of the main issues that we did see yesterday was the spread of mis- and disinformation.”

Kent Volkmer, the attorney for Pinal County, said there were more in-person voters in the county than had been seen before, including far more independent voters. He added that many voters surrendered their mail-in ballot so they could vote in person, possibly motivated by the ballot-printing issues.

“We don’t think that there’s nearly as many people who were negatively impacted as what’s being related to the community,” Mr. Volkmer said.

One common talking point on Tuesday resurrected a false theory from 2020, known as Sharpiegate, which claimed that markers offered by poll workers were bleeding through and invalidating ballots. Election officials have said that machines can read ballots marked with pens, markers and other instruments, and any issues can be reviewed manually.

“This is Sharpiegate 2.0,” Ben Berquam, a conservative commentator, said on a livestream. Mr. Finchem shared the conspiracy theory on his Twitter account. The campaign for Ron Watkins, a congressional candidate for Arizona’s Second District who came in last place in his race on Tuesday, also suggested that Mr. Watkins’s votes were being artificially slashed.

Many election fraud theories focused on the governor’s primary race between Kari Lake, the Trump-endorsed former news anchor, and Karrin Taylor Robson, who was endorsed by former Vice President Mike Pence. Ms. Lake was badly trailing her competitor for most of the night, whipping up election fraud theories among her supporters. She eventually took the lead.

Ms. Lake’s allies suggested during a livestream that the results were suspicious because many other Trump-aligned candidates were winning their races. In Arizona, mail-in ballots received before Election Day are counted first, and polling suggested those would slightly favor Ms. Taylor Robson. In-person votes were counted on election night, and Ms. Lake’s supporters preferred voting in person.

As counting continued late into the night, Ms. Lake claimed victory while she was still trailing Ms. Taylor Robson.

“When the legal votes are counted, we’re going to win,” Ms. Lake said at her election night party. The Associated Press has not yet called the race.