It is the third time the division under Attorney General Merrick B. Garland has challenged a state’s election law and comes as Democratic leaders and voting rights groups have pressed Mr. Garland to act more decisively against measures that limit ballot access. The Arizona law, signed by Gov. Doug Ducey, a Republican, in March, requires voters to prove their citizenship to vote in presidential elections, such as showing a birth certificate or passport. It also requires newly registered voters to provide proof of address, which could disproportionately affect people with limited access to government-issued ID cards. These include immigrants, students, seniors, low-income voters, and Native Americans. “Arizona passed a law that turns back the clock by imposing illegal and unnecessary requirements that would keep eligible voters off the registration rolls for certain federal elections,” Kristen Clarke, assistant attorney general for the Justice Department’s civil rights division, told reporters. Tuesday. Ms. Clark said that by imposing what she described as “burdensome” prerequisites, the law “constitutes a textbook violation” of the National Voter Registration Act, which makes it easier to register to vote. The department said the law also violated the Civil Rights Act of 1964 by requiring election officials to reject voter registration forms based on errors or omissions unrelated to a voter’s eligibility. As of March, 31,500 “federal only” voters could be prevented from voting in the next presidential election under the new requirements if state officials can’t track down their information in time to validate their ballots. Some voting rights groups argue that the number of affected voters could be even higher. But even a few thousand fewer votes could be decisive in Arizona, one of the most closely contested states in the battleground: In 2020, Joseph R. Biden Jr. defeated President Donald J. Trump in Arizona by about 10,000 votes. A spokesman for Mr. Ducey did not immediately respond to requests for comment. When he signed the bill in March, Mr. Ducey said the law, expected to take effect in January, was “a balanced approach that honors Arizona’s history of making voting accessible without sacrificing the security of our elections.” . Arizona has been at the center of some of the most contentious battles in the 2020 election. Six months after the election, its Republican-led Senate approved an outside review of the Maricopa County election, an anomalous step that quickly became a flashpoint for the conspiracy theorists. The state has also passed several laws imposing new restrictions on voting. Even before the Republican-controlled Legislature passed the measure, existing state law required all voters to show proof of citizenship to vote in state elections. Federal voter registration forms still required voters to certify that they were citizens, but not to provide proof of identity. In 2013, the Supreme Court upheld that law, but added that Arizona must accept the federal voter registration form for federal elections. This effectively created a split system in Arizona that would require documentary proof of citizenship to vote in state elections, but would allow those who simply sign up for federal voter registration to be able to vote in federal elections. The new law could threaten those voter registrations, preventing tens of thousands of them from voting in the presidential election, voting rights groups argue. “There will certainly be some people in Arizona who will not be able to vote under the proof of citizenship requirement,” said Jon Greenbaum, the chief counsel of the nonpartisan Lawyers’ Committee on Civil Rights Under Law and a former attorney for the Justice Department. While the new law would have huge implications for many groups, local elections officials have noted that providing proof of citizenship could be especially difficult for Native Americans, who were key to helping Arizona in Mr. Biden in 2020. “You can have people who were born on reservations who may not have birth certificates, and so it can be very difficult to prove citizenship in some way,” said Adrian Fontes, the former Maricopa County elections administrator and a current Democratic nominee for secretary. of the state. “Things of this nature have always been of great concern to election administrators in Arizona.” In June 2021, the department sued Georgia over the new election law that overhauled the state’s election administration and introduced a number of restrictions on voting in the state, especially voting by mail. In November, the department sued Texas over a provision limiting assistance given to voters at the polls. Marc Elias, a Democratic election lawyer who represented a group that filed a lawsuit against Arizona earlier this year, said he was relieved to see the department follow through on Mr. Biden’s pledge last year to address a threat from state laws that supported by Republicans. the “most important test of democracy” since the Civil War. “Adding the voice and authority of the United States is incredibly helpful in the fight for voting rights,” Mr. Elias said in an interview.