A Democratic legal fight against restrictive voting laws enacted in recent years by Republican-controlled state governments is being largely paid for by a single liberal benefactor: the billionaire philanthropist George Soros.

Mr. Soros, the Hungarian-born investor whose first major involvement in American politics was a voter-mobilization drive in the 2004 presidential race, has yet to commit the many millions of dollars that Hillary Rodham Clinton’s allies hope he and other like-minded billionaires will pour into the “super PAC” directly aiding her campaign.

But it turns out that Mr. Soros has already agreed to put as much as $5 million into the litigation effort, which Democrats hope will erode restrictions on voter access that they say could otherwise prove decisive in a close election.

The lawsuits — which are being led by a lawyer whose clients include Mrs. Clinton’s campaign — are attacking a variety of measures, including voter-identification requirements that Democrats consider onerous, time restrictions imposed on early voting that they say could make it difficult to cast ballots the weekend before Election Day, and rules that could nullify ballots cast in the wrong precinct.

The lawyer, Marc Elias, who specializes in voter-protection issues, was in contact with Mr. Soros in January 2014 when Mr. Elias was exploring a series of federal lawsuits before that year’s midterm election and in advance of the 2016 campaign, according to Mr. Soros’s political adviser, Michael Vachon. (Mr. Elias declined to comment on Friday about the funding of the lawsuits.)

The goal is to try to influence voting rules in states where Republican governors and Republican-led legislatures have enacted election laws since 2010, and to be ready to intervene if additional measures are passed over the next 17 months.

Mr. Soros described himself as “proud” to be part of the legal battles. “We hope to see these unfair laws, which often disproportionately affect the most vulnerable in our society, repealed,” he said.

Two suits that Mr. Soros is supporting were filed in Ohio and in Wisconsin last month. He is also helping to pay for a case that Mr. Elias and several other groups filed last year in North Carolina.

Democrats say the new laws disproportionately affect the poor, minorities and young people. A Government Accountability Office study last October found that states with more stringent voter identification laws had a larger decline in voter turnout than states that did not have such new restrictions.

Republicans have argued that the new laws are much-needed protection against election fraud, and dismiss the litigation — which could soon expand to cases in Georgia, Nevada and Virginia, Democrats say — as little more than a gambit to energize minority voters in support of Democratic candidates.

But Mr. Vachon described it as an attempt to push back at Republicans who he said were “using the legislative process” for partisan purposes.

“It is disingenuous to suggest that these laws are meant to protect against voter fraud, which is nearly nonexistent,” he said. “Clearly they are meant to give Republicans a political advantage on Election Day.”

Mr. Elias’s clients include four major national Democratic Party committees — as well as the Clinton presidential campaign, which is not a party to the lawsuits, though her team has spoken favorably of them.

But Mrs. Clinton seized on voting rights this week, attacking some of her potential Republican opponents in a speech in Houston on Thursday for voting laws enacted in their states, and calling for automatic voter registration nationwide when people turn 18.

“I call on Republicans at all levels of government with all manner of ambition to stop fear-mongering about a phantom epidemic of election fraud and start explaining why they’re so scared of letting citizens have their say,” Mrs. Clinton said.

Some of the Republicans she named, notably Gov. Chris Christie of New Jersey and Gov. Scott Walker of Wisconsin, responded in kind.

“Secretary Clinton doesn’t know the first thing about voting rights in New Jersey or in the other states that she attacked,” Mr. Christie said, according to The Record newspaper of Hackensack, N.J. “My sense is that she just wants an opportunity to commit greater acts of voter fraud around the country.”

And Mr. Walker said Mrs. Clinton’s “rejection of efforts to make it easier to vote and harder to cheat not only defies logic, but the will of the majority of Americans.”

Mr. Soros’s first foray into Democratic politics came in 2004, when he provided millions of dollars to try to unseat President George W. Bush, including through a voter mobilization drive called America Coming Together.

While Mr. Soros has not pledged money to the super PAC focused solely on Mrs. Clinton, Mr. Vachon said he has given $1 million this year to the research-focused super PAC American Bridge. The legal actions filed by Mr. Elias are in keeping with the type of advocacy Mr. Soros has favored: efforts at the nexus of policy, politics and movement-building.

Mr. Vachon said Mr. Elias first approached him early last year about supporting a voting rights lawsuit in North Carolina, where student identification cards are not considered acceptable forms of photo ID. The restrictions in North Carolina ended a program in which teenagers filled out a form and were then registered automatically to vote on their 18th birthday. Joining with the N.A.A.C.P., the Justice Department and the American Civil Liberties Union, Mr. Elias argued that the law was onerous for younger voters in violation of the 26th Amendment, which lowered the voting age to 18 from 21.

The North Carolina case is still pending.

But Mr. Elias and Mr. Vachon have discussed filing other suits in some of the 21 states that have added voting restrictions since the 2010 Republican electoral wave, if those states seek to tighten voting access any further.

“I expect there will be more,” Mr. Vachon said.