WASHINGTON—Republican candidates for governor and secretary of state who have echoed former President Donald Trump’s false claims that the 2020 election was rife with fraud have proposed changes in voting access and election certification that could have ramifications in key states in the next presidential election.

Seven Republicans running for those offices in Pennsylvania, Wisconsin, Arizona, Michigan and Nevada—all presidential battlegrounds—haven’t all detailed how they would oversee the 2024 election but have publicly touted measures they say would ensure election integrity, as they question the outcome of the 2020 race. Federal authorities have said there was no widespread fraud that would have changed the result, and several court challenges by the Trump campaign failed. All states certified President Biden’s victory.

SHARE YOUR THOUGHTS

Which governor races are you looking at closely this year and why? Join the conversation below.

Some of the changes the candidates support, such as tightening voter-identification rules or limiting absentee voting, align with measures Republicans have already passed or have been seeking to pass in other states. Other ideas they have floated go further.

Republican Kari Lake, who is in a race viewed as a tossup for governor in Arizona, has called for decertifying the results of the 2020 election in some close-run states including Arizona, which Mr. Biden won by just over 10,000 votes. The state’s Republican candidate for secretary of state, Mark Finchem, co-sponsored a bill that calls for state lawmakers to review the ballot tabulating process and accept or reject election results. It also would require election workers to count ballots by hand rather than relying on vote-counting machines. He is running against Democrat Adrian Fontes.

In Pennsylvania, Republican gubernatorial candidate Doug Mastriano has said he could require everyone to re-register to vote if he were to win. He currently trails Democrat Josh Shapiro substantially in most polls. Such a move would violate federal law, said David Becker, executive director of the nonpartisan Center for Election Innovation and Research. Mr. Mastriano didn’t respond to a request for comment.

Doug Mastriano, a gubernatorial candidate in Pennsylvania, has suggested requiring everyone to re-register to vote if he wins.

Photo: Mark Makela/Getty Images

In Wisconsin, Republican Tim Michels, who is in a tight race with Democratic Gov. Tony Evers, said on his campaign website that he would call for a special legislative session “to fix the election mess and ensure the integrity of every single ballot.” He has called for replacing the Wisconsin Elections Commission, repealing all of its previous election guidance, and purging the voting rolls of dead and inactive voters twice a year. State law in Wisconsin requires the commission to conduct voter-list maintenance every two years after the fall elections by contacting people who haven’t voted in the past four years and deactivating them if they don’t respond or don’t wish to remain registered.

The powers of governors and secretaries of state vary by state, but they generally have influence in overseeing elections and certifying results, as well as the process for awarding electoral votes in presidential elections. Some changes would require action from state legislatures, which governors could support or veto. Any new measures could also be challenged in court.

Since Mr. Biden’s victory, voting access and the integrity of elections have been contentious topics in Washington and at the state level. Democratic officials in states including Michigan, Pennsylvania and Wisconsin blocked efforts by some Republicans to overturn the 2020 election results. Some Republican officials in Georgia and Arizona withstood pressure from within their party to not certify the result of the vote. Congressional Democrats introduced legislation to govern elections nationwide, but the move lacked sufficient Senate support to move forward.

Several Republican-led states, meanwhile, introduced new voting laws. In Georgia, Gov. Brian Kemp has signed legislation that altered how people vote absentee and where people can drop off their ballots. Mr. Kemp is running for re-election against his 2018 opponent, Democrat Stacey Abrams. She alleged that he unfairly restricted voting access in that election, and she didn’t concede the race, though she acknowledged Mr. Kemp as governor.

Georgia Gov. Brian Kemp has signed legislation that changed absentee voting and where people drop off their ballots.

Photo: Dustin Chambers/Bloomberg News

Republicans say the changes they have made are needed to improve the electoral system or roll back pandemic-related changes they contend are no longer necessary. Democrats say that many of the moves by Republican-led states will have the effect of reducing access and options for voters, especially in minority communities. They also say governors and secretaries of state who deny the results of the 2020 election pose a particular threat to the integrity and confidence in future voting.

“Republican candidates who deny elections but become governor can wreak havoc on the system and threaten democracy itself,” said North Carolina Gov. Roy Cooper, who is chairman of the Democratic Governors Association, which supports Democratic candidates for governor.

Jesse Hunt, a spokesman for the Republican Governors Association, the campaign arm for GOP governors, noted that every Republican governor certified the 2020 election results. “What you’re seeing right now from Democrats is an attempt to distract from the very real problems that people have,” on issues such as inflation, crime and the economy that are at the top of voters’ minds heading into the Nov. 8 midterm elections, he said.

Mark Finchem, an Arizona secretary of state candidate, co-sponsored a bill that calls for state lawmakers to review ballot tabulating.

Photo: Ash Ponders for The Wall Street Journal

Republicans in several states questioned whether voting machines were secure or ballots counted correctly in 2020. A GOP-commissioned review of the presidential election results in Arizona’s most-populous county didn’t change Mr. Biden’s victory there. A hand recount in Georgia confirmed Mr. Biden’s win in that state.

Ms. Lake, the candidate for Arizona governor, and Mr. Finchem, the secretary of state candidate, filed an unsuccessful lawsuit seeking to bar the use of electronic vote-counting machines in the midterm elections, a move they argue is aimed at improving security. Mr. Becker of the Center for Election Innovation and Research said hand-counting ballots is more costly and time-consuming and less accurate than relying on electronic machines.

Mr. Finchem was near the U.S. Capitol on Jan. 6, 2021, when Trump supporters rioted in a bid to prevent lawmakers from certifying Mr. Biden’s victory. He said in a recent debate he was there to deliver a book of information on election irregularities to a congressman. He also said during a debate that he had been interviewed as a witness by the Justice Department and the congressional committee investigating the events. He hasn’t faced federal charges.

Mr. Mastriano, the Pennsylvania candidate for governor, was subpoenaed by the congressional committee earlier this year. The committee said it was interested in efforts to arrange for an alternative slate of electors from Pennsylvania and in what he saw near the Capitol on Jan. 6. Mr. Mastriano filed suit to block the subpoena. His attorney said the committee didn’t have the authority to compel testimony because its top Republican wasn’t appointed by the party’s congressional leadership.

Write to Catherine Lucey at catherine.lucey@wsj.com and Ken Thomas at ken.thomas@wsj.com