Arizona county election officials have identified fewer than 200 cases of potential voter fraud out of more than 3m ballots cast in last year’s presidential election, undercutting Donald Trump’s claims of a stolen election as his allies continue a disputed ballot review in the state’s most populous county.

The 182 cases identified by the Associated Press represent instances where problems were clear enough that officials referred them for further review. So far, only four cases have led to charges, including those identified in a separate state investigation. No one has been convicted. No vote was counted twice.

More cases could emerge but the numbers illustrate the implausibility of Trump’s claims that fraud and irregularities cost him the state. In final, certified and audited results, Joe Biden won 10,400 more votes in Arizona than Trump out of 3.4m cast.

The AP findings align with previous studies showing voter fraud is rare. Numerous safeguards are built into the system to prevent and detect it.

“The fact of the matter is that election officials across the state are highly invested in helping to ensure the integrity of our elections and the public’s confidence in them,” said Arizona’s secretary of state, Katie Hobbs, a Democrat. “And part of that entails taking potential voter fraud seriously.”

Of the four Arizona cases that have resulted in criminal charges, two involved Democratic voters and two Republicans.

The AP review supports statements made by state and local elections officials, as well as Republican county officials and Governor Doug Ducey, that Arizona’s presidential election was secure and its results valid.

Still, Arizona’s Republican-led state Senate has for months been conducting a “forensic audit” in Maricopa county, which covers Phoenix. The effort has been discredited by election experts and faced bipartisan criticism but some Republicans, including Trump, have suggested it will uncover widespread fraud.

“This is not a massive issue,” said Adrian Fontes, a Democrat who oversaw the Maricopa county election office during the 2020 election and lost his re-election bid. “It is a lie that has developed over time. It’s been fed by conspiracy theorists.”

The AP tallied the potential cases after submitting public record requests to all Arizona counties. Eleven out of 15 reported no potential cases. The majority of cases identified involve people casting a ballot for a relative who died or people who tried to cast two ballots.

An election integrity unit of the state attorney general’s office created in 2019 has been reviewing potential cases of fraud. A spokesperson for the attorney general, Mark Brnovich, told the AP in April the unit had 21 active investigations, although he did not specify if all were from last fall. A month later, the office indicted a woman for casting a ballot on behalf of her dead mother. A spokesperson declined to provide updated information this week.

Maricopa county has identified just one case of potential fraud out of 2.1m ballots cast. That was a voter who might have cast a ballot in another state. The case was sent to the county attorney’s office, which forwarded it to the state attorney general.

Virtually all the cases identified by county officials are in Pima county, home to Tucson, and involved voters who attempted to cast two ballots. The Pima recorder’s office has a practice of referring all cases with even a hint of fraud to prosecutors for review, something the state’s 14 other county recorders do not do.

Pima officials forwarded 151 cases. They did not refer 25 from voters over age 70 because there was a greater chance those errors were the result of memory lapses or confusion, not criminal intent, an official said. None of the 176 duplicate ballots was counted twice.

An unusually high number of people appeared to have intentionally voted twice, often by voting early in person and then by mail. The Pima county deputy recorder, Pamela Franklin, noted several factors, including worries about US Postal Service delays.

In addition, Trump at one point encouraged voters who cast their ballots early by mail to show up at their polling places on election day and vote again if poll workers could not confirm their mail ballots had been received.

The results in Arizona are similar to early findings in other battleground states. Officials in Wisconsin identified just 27 potential cases of fraud out of 3.3m ballots cast last November, according to records obtained by the AP.

The AP conducted the review following months of Trump and his allies claiming without proof he won the 2020 election. His claims of widespread fraud have been rejected by election officials, judges, election security officials and even his own attorney general.

Even so, supporters repeat them and they have been cited by state lawmakers as justification for tighter voting rules.

In Arizona, Republicans have used the unsubstantiated claims to justify the unprecedented review of the election in Maricopa county and to pass legislation that could make it harder for infrequent voters to receive mail ballots automatically.