ALBUQUERQUE, N.M. — Two candidates vying to become New Mexico’s top elections and campaign finance regulator used a debate on Sunday morning to present sharply different visions of how to run the New Mexico Secretary of State’s Office.

Republican Nora Espinoza, a former teacher and member of the state House of Representatives for the past decade, emphasized her intention to safeguard the integrity of the voting system against concerns of voter fraud, attacking her Democratic opponent’s administrative record as a county clerk at nearly every turn in an hourlong debate.

“The foundation of this process is voter ID,” said Espinoza, who supports legal changes to require photo identification when voting in person, with limited exceptions for Native American voters. “People, once they see that the system is honest and fair for all — whether you’re a Republican, Democrat, or independent — they will turn out.”

The Democratic candidate, Bernalillo County Clerk Maggie Toulouse Oliver, accused her opponent of attempting to suppress voter participation in a state where registered Democrats significantly outnumber Republicans, and she touted her knowledge and experience in administering elections in New Mexico’s most populous county since 2007. The Secretary of State’s office oversees a balloting system that relies heavily on elected clerks in 33 counties to run elections and update voter registration rolls.

“Democracy should encourage and foster voter participation across the spectrum,” Toulouse Oliver said. “My opponent is sadly much more interested in keeping people from voting than encouraging people to participate.”

The victor in the November general election will fill the remainder of a term vacated by former Secretary of State Dianna Duran. The Republican former county clerk resigned last year and pleaded guilty to felony counts of embezzlement and money laundering, serving a month in jail after acknowledging she used campaign funds to fuel a gambling spree.

Toulouse Oliver unsuccessfully challenged Duran in 2014, in campaigning that hinged on similar themes as this year.

Espinoza on Sunday accused Toulouse Oliver of creating new potential for voter fraud by sending out electronic voter-identification bar codes on postcards to registered voters in Bernalillo County ahead of this year’s primary and general election.

Toulouse Oliver said the bar codes are tied to individual voter records and allow poll workers to quickly call up those records and reduce wait times, without changing requirements for identification or felony penalties for falsifying registration or ballot information. The postcards, she said, provide basic information about where, how and when to vote and are used with bar codes in at least two other counties.

Toulouse Oliver said she would seek to restore straight party-ticket voting, where a slate of Democratic or Republican candidates can be chosen at one time. The option was removed during Duran’s tenure. She also wants to open primary elections for major party candidates to voters who are not affiliated with the GOP or Democratic Party. Espinoza says those issues should be decided by the Legislature.

Several exchanges between Toulouse Oliver and Espinoza echoed a heated national debate on voting rights and procedures, as many Republican-controlled legislatures seek to tighten voter laws by limiting same-day registration and early voting and by requiring IDs at polling places.

In 2013, the U.S. Supreme Court invalidated a key provision of the 1965 Voting Rights Act, which required mostly Southern states with a history of discrimination to get advance federal approval to change election laws. The decision made it easier for states to impose new restrictions.

Democrats in the New Mexico state Legislature have largely held at bay proposals for stricter voter identification requirements. Espinoza introduced an unsuccessful bill this year that would have required photo identification to vote in person and expanded identification requirements for absentee voting by mail or in person.

“I am for every eligible voter to be able to vote but not to set up a process where there can be this voting fraud, where it encourages ineligible voters to vote,” Espinoza said.

Toulouse Oliver criticized “haphazard” efforts tighten voter identification provisions. She said New Mexico can ill afford during a budget crisis to join other states in costly litigation to defend onerous identification provisions.

“I support and have supported in the past any legislation that enhances the integrity of our election process, but not at the cost of disenfranchising otherwise eligible citizens to vote,” she said.