The federal government is processing citizenship requests at the fastest clip in a decade, moving rapidly through a backlog that built up during the Trump administration and the coronavirus pandemic.

At ceremonies in courthouses, convention centers and sports arenas across the country, thousands of immigrants are becoming new Americans every week — and becoming eligible to vote in time for the presidential election this fall.

It’s unclear how many of the new voters live in battleground states, but a number of the states where Kamala Harris or Donald Trump must win have large and growing numbers of voting-age naturalized citizens, including Georgia, Arizona, Nevada and Pennsylvania.

In Savannah, Ga., people from 19 countries streamed into a federal courthouse recently to take the oath of allegiance.

“My case was done in less than six months,” said Gladis Brown, who is married to an American and emigrated from Honduras in 2018.

Generally, lawful permanent residents, known as green-card holders, are eligible to become naturalized citizens if they have had that status for at least five years, or have been married to a U.S. citizen for at least three years.

Green-card holders have many of the same rights as citizens. But voting in federal elections is a right accorded only to citizens. And that can be a powerful motivation to pursue citizenship, especially when big national elections are on the horizon.

“I’m so glad that the process moved quickly,” said Ms. Brown, who was one of the 31 immigrants being sworn in. “People like me want to vote in the election.”

After the ceremony, Ms. Brown celebrated with cake and punch from a local women’s volunteer group — and by completing a voter-registration form provided by a representative of the League of Women Voters.

Naturalization applications typically spike upward in the approach to an election.

“The surge in naturalization efficiency isn’t just about clearing backlogs; it’s potentially reshaping the electorate, merely months before a pivotal election,” said Xiao Wang, chief executive of Boundless, a company that uses government data to analyze immigration trends and that offers services to immigrants who seek professional help in navigating the application process.

“Every citizenship application could be a vote that decides Senate seats or even the presidency,” Mr. Wang said.

At under five months, application processing speed is now on a par with 2013 and 2014. About 3.3 million immigrants have become citizens during President Biden’s time in office, with less than two months to go before the close of the 2024 fiscal year.

The U.S. Citizenship and Immigration Services took 4.9 months, on average, to process naturalization applications in the first nine months of the current fiscal year, compared with 11.5 months in fiscal 2021.

After taking office in 2021, Mr. Biden issued an executive order that sought to dial back his predecessor’s hard-line immigration agenda and “restore faith” in the legal immigration system. Among other steps, the order called for action to “substantially reduce current naturalization processing times” with the goal of strengthening integration of new Americans.

Unlike many federal agencies, the citizenship agency is funded mainly by fees paid by applicants, rather than by congressional appropriations, giving the administration latitude to define its priorities and the allocation of resources.

The Biden administration began deploying new technology and additional staff in 2022 to reduce the pending caseload of citizenship applications, which had ballooned because of heightened scrutiny by the Trump administration and protracted pandemic-related delays in conducting the swearing-in ceremonies.

The Biden administration also shortened the naturalization application to 14 pages from 20. It raised the application fee in April to $710 from $640, but made it easier for low-income people to qualify for a discount.

While there has long been partisan disagreement over how to tackle illegal immigration and overhaul the nation’s immigration laws, naturalizing lawful residents had broad bipartisan support.

As president, George W. Bush signed an executive order in 2002 expediting naturalization for noncitizens serving in the military. Since he left office, he has hosted oath ceremonies at his institute in Dallas.

But citizenship has become more politicized in recent years.

Intent on curbing legal immigration, the Trump administration conducted lengthier reviews of naturalization applications. The processing time roughly doubled to about 10 months during Mr. Trump’s tenure.

The bottleneck prevented some 300,000 prospective citizens from naturalizing in time to vote in the 2020 election, according to estimates by Boundless.

Some nine million green-card holders are currently eligible to become U.S. citizens, according to the latest official data. Naturalized Latinos, who make up the largest share of the new citizens, have historically leaned Democratic, as have naturalized Asians and Africans, according to Louis DeSipio, a political scientist at the University of California, Irvine, who studies voter behavior.

Citizenship confers benefits and legal protections. Citizens cannot be deported; green-card holders convicted of crimes can be sent back to their country of origin.

The four states with the largest number of immigrants who qualify for citizenship are California, New York, Texas, and Florida. Mexico, India, the Philippines, the Dominican Republic and Cuba are the top countries of origin.

While immigrants cite the right to vote as an important factor in their decision to naturalize, the reality is that many do not register, or do not cast ballots. Overall, naturalized citizens have a lower registration rate than native-born Americans.

“There has to be investment to turn them out, from the parties, churches, unions,” Dr. DeSipio said. “If you make an effort to turn them out, then they turn out.”

The NALEO Educational Fund, a nonpartisan organization that promotes Latino civic engagement, operates a hotline that it publicizes on Spanish-language media. The hotline helps people register and answers questions about mail-in ballots, polling stations and other election matters.

“People want to participate in our democracy, but they hit a wall when they don’t have the information they need,” said Juan Rosa, director of civic engagement at the fund.

A recent survey suggested that there was enthusiasm for voting in November.

Among naturalized citizens, 81.4 percent said they “definitely” would cast a ballot in the 2024 election, and another 14.5 percent said they “probably” would vote, according to the survey, which was conducted by the U.S. Immigration Policy Center at the University of California, San Diego, with the National Partnership for New Americans.

“The American electorate is as diverse as it has ever been, and much of that has been fueled by newly naturalized citizen voters, who are making up an increasingly large share of the electorate,” said Tom Wong, a political scientist at the university who led the study.

The oath of allegiance is the last step to obtaining U.S. citizenship, after passing a background check, health exam, interview and civics test.

In the Savannah federal courthouse, R. Stan Baker, the chief judge, shook hands and posed for a photo with each person who was sworn in. “You have the full rights of an American,” he said. “Don’t let anyone tell you otherwise.”

As the new Americans emerged from the courtroom, Chassidy Malloy of the League of Women Voters of Coastal Georgia approached several of them, offering voter registration forms.

Some left clutching the form, along with their citizenship certificate and a small American flag.

Others chose to register on the spot, including three members of the Patel family.

“This is a wonderful country that we want to be fully a part of,” said Nishang Patel, 28, a dentist born in Kenya who arrived in the United States as a child. “We will contribute and vote,” he said. ##