WASHINGTON — In Georgia, Arizona and other states won by President Biden, some leading Republicans stood up in November to make what, in any other year, would be an unremarkable statement: The race is over. And we lost, fair and square.

But that was then. Now, in statehouses nationwide, Republicans who echoed former President Donald J. Trump’s baseless claims of rampant fraud are proposing to make it harder to vote next time — ostensibly to convince the very voters who believed them that elections can be trusted again. And even some colleagues who defended the legitimacy of the November vote are joining them.

According to the Brennan Center for Justice at New York University, state legislators have filed 106 bills to tighten election rules, generally making it harder to cast a ballot — triple the number at this time last year. In short, Republicans who for more than a decade have used wildly inflated allegations of voter fraud to justify making it harder to vote, are now doing so again, this time seizing on Mr. Trump’s thoroughly debunked charges of a stolen election to push back at Democratic-leaning voters who flocked to mail-in ballots last year.

In Georgia, where the State House of Representatives has set up a special committee on election integrity, legislators are pushing to roll back no-excuse absentee voting. Republicans in Pennsylvania plan 14 hearings to revisit complaints they raised last year about the election and to propose limitations on voting.

Arizona Republicans have subpoenaed November’s ballots and vote tabulation equipment in Maricopa County, a Democratic stronghold that includes Phoenix. Legislators are taking aim at an election system in which four in five ballots are mailed or delivered to drop boxes.

Those and other proposals underscore the continuing power of Mr. Trump’s campaign to delegitimize the November election, even as some of his administration’s top election experts call the vote the most secure in history. And they reflect longstanding Republican efforts to push back against efforts to expand the ability to vote.

Democrats have their own agenda: 406 bills in 35 states, according to the Brennan Center, that run the gamut from giving former felons the vote to automatically registering visitors to motor vehicle bureaus and other state offices. And Democrats in the Senate will soon unveil a large proposal to undergird much of the election process with what they call pro-democracy reforms, with lowering barriers to voting as the centerpiece. Near-identical legislation has been filed in the House.

“There’s going to be a rush in the next year to legislate certain types of election reforms,” said Nate Persily, a Stanford University law professor and co-director of the Stanford-MIT Healthy Elections Project. “The jury is still out on whether the lesson from this election will be that we need to make voting as convenient as possible, or whether there will be a serious retrenchment that makes voting less accessible.”

In truth, who controls a given legislature will largely decide what chances a bill has.

In the 23 states wholly run by Republicans, Democratic bills expanding ballot access are largely dead on arrival. The same is true of Republican proposals to restrict ballot access in the 15 states completely controlled by Democrats.

But in some states where legislators’ control and interests align, the changes could be consequential.

In Arizona, where Democrats captured a second Senate seat and Mr. Biden eked out a 10,500-vote victory, lawmakers are taking aim at an election system in which absentee ballots have long been dominant.

One bill would repeal the state’s no-excuse absentee ballot law. Others would pare back automatic mailings of absentee ballots to the 3.2 million voters who have signed up for the service. One ardent advocate of the stolen-election conspiracy theory, State Representative Kevin Payne of Maricopa County, would require that signatures on all mail ballots be notarized, creating an impossibly high bar for most voters. Yet another bill, paradoxically, would require early ballots that are mailed to voters to be delivered by hand.

In Georgia, where Mr. Biden won by fewer than 12,000 votes, Secretary of State Brad Raffensperger and Gov. Brian Kemp, both Republicans, have repeatedly defended the election results. The two are nevertheless supporting stricter voting requirements.

A proposal by Republicans in the State Senate to eliminate no-excuse absentee ballots — a quarter of the five million votes cast in November — has drawn opposition even before it has been filed. But Republicans broadly support a bill to require submitting a photocopied identification card such as a driver’s license with both applications for absentee ballots and the ballots themselves. Mr. Raffensperger has said he supports that measure and another to make it easier to challenge a voter’s legitimacy at the polls.

Brian Robinson, a Republican political consultant in Atlanta, said, “The overall purpose of these reforms is to restore faith in our election systems.” He added, “That’s not to say that it was a giant failure; that’s to say that faith has been diminished.”

He allowed that Mr. Trump’s false charges of fraud “drives a lot of the loss of faith among Republicans,” but he also took aim at Democrats, noting that the Democrat who lost the 2018 governor’s race, Stacey Abrams, also had refused to concede, saying voter suppression had caused an “erosion of our democracy.”

“Both sides have dipped their toes in those waters,” he said.

But it’s clear that Republicans are now dipping much more than their toes. Democrats and some voting-rights advocates say the Republican agenda on voting is less about lost trust than lost elections. A Republican election official in suburban Atlanta said as much this month, arguing for tougher voting laws that reduce turnout after Democratic candidates won both of the state’s Senate seats in runoffs.

“They don’t have to change all of them,” said Alice O’Lenick, who heads the Gwinnett County Board of Registrations and Elections, “but they have got to change the major parts of them so we at least have a shot at winning.”

Marc Elias, a Democratic lawyer who led legal battles against restrictive voting rules last year, said the reason for the state’s voting-law crackdown was transparent. “These were elections that withstood the scrutiny of two recounts, an audit and a whole lot of attention in the political arena and the courts,” he said. “The only reason they’re doing this is to make voting harder because they didn’t like the results. And that’s shameful.”

Indeed, a handful of bills seem to make no bones about their partisan goals. One Arizona proposal would give the Legislature the power to decide presidential elections by overriding the secretary of state’s certification of electoral votes.

Bills in Arizona, Mississippi and Wisconsin would end the practice of awarding all electoral votes to the presidential candidate who wins the statewide vote. Instead, they would be allotted according to votes in congressional districts — which in Republican states are generally gerrymandered to favor Republicans. In Arizona, the Legislature also would choose two electors.

In the last election, the moves would have reduced Mr. Biden’s electoral vote total by 11 votes.

Nebraska, on the other hand, would do the reverse with a similar partisan outcome: The state now awards presidential electors by congressional district, but legislation would move the state to the winner-take-all system. One of Nebraska’s three House districts voted for Mr. Biden in November.

Even Republicans in states where the November election was not close are proposing to tighten voting laws. In Texas, a state with perhaps the nation’s strictest voting rules and one of the lowest levels of turnout, the state party has declared “election integrity” the top legislative priority. Among other proposals, legislators want to cut the time allotted for early voting, limit outsiders’ ability to help voters fill out ballots and require new voters to prove they are citizens.

Republicans who control the Pennsylvania Legislature have mounted one of the most aggressive campaigns, even though any laws they enact probably would have to weather a veto by the state’s Democratic governor.

A handful of Republican state lawmakers want to abolish no-excuse absentee voting only 15 months after the Legislature approved it in an election-law package backed by all but two of its 134 G.O.P. members who cast votes. The main supporter of the bill, State Senator Doug Mastriano, has claimed that Mr. Biden’s victory in the state is illegitimate, and spent thousands of dollars to bus protesters to the Jan. 6 demonstration that ended in the assault on the Capitol.

Rolling back the law appears a long shot. But there seems to be strong Republican support for other measures, including eliminating drop boxes for absentee ballots, discarding mail-in ballots with technical errors and ending a grace period for receiving ballots mailed by Election Day.

State Representative Seth Grove, the Republican chair of the committee holding 14 hearings into election practices, said at the initial gathering on Jan. 21 that he was not interested in dwelling on the 2020 election. “We want a better process going forward, and we’re committed to that,’’ Mr. Grove said.

But at that hearing, legislators grilled Secretary of State Kathy Boockvar, a Democrat, for three hours on her emailed guidance to county election officials before the Nov. 3 vote.

In an interview, Ms. Boockvar said the purpose of the hearings was to further undermine voters’ confidence in democracy and to “lay the groundwork for disenfranchisement.’’

“We are at a watershed, and we have a choice to make right now,” she said. “Acknowledge the truth — have public, vocal, strong support for the strength and resilience of our democracy. Or we can continue to perpetuate the lies.”

In Washington, a Democratic agenda can be seen in the latest version of a far-ranging elections and voting bill that passed the House last year but died in the Republican-controlled Senate.

This time, the Democrat-controlled Senate will file its own version, with committee hearings expected in February.

Its voting provisions include allowing automatic and same-day voter registration, 15 days of early voting, no-excuse voting by mail, and online voter registration, as well as the restoration of voting rights nationwide to felons who complete their sentences. In one fell swoop, it would set minimum standards for American federal elections that would erase a host of procedural barriers to casting a ballot.

It also would require the states to appoint independent and nonpartisan commissions to draw political boundaries, eliminating the profusion of gerrymanders that the Supreme Court said in 2019 were beyond its authority to control.

Few expect much chance of passage in a deeply divided Senate, but the Democratic leaders in both houses have made it the first bill of the new congressional session, a statement that — symbolically, at least — it is the first priority of the new Democratic majority.

Whether any of it goes beyond symbolism remains to be seen.

Trip Gabriel contributed reporting.