WASHINGTON — The Supreme Court seemed ready on Tuesday to uphold two election restrictions in Arizona and to make it harder to challenge all sorts of limits on voting around the nation.

In its most important voting rights case in almost a decade, the court for the first time considered how a crucial part of the Voting Rights Act of 1965 applies to voting restrictions that have a disproportionate impact on members of minority groups. The court heard the case as disputes over voting rights have again become a flash point in American politics.

The immediate question for the justices was whether two Arizona measures ran afoul of the 1965 law. One of the measures requires election officials to discard ballots cast at the wrong precinct. The other makes it a crime for campaign workers, community activists and most other people to collect ballots for delivery to polling places, a practice critics call “ballot harvesting.”

Several members of the court’s conservative majority said the restrictions were sensible, commonplace and at least partly endorsed by a bipartisan consensus reflected in a 2005 report signed by former President Jimmy Carter and James A. Baker III, who served as secretary of state under President George Bush.

The Biden administration, too, told the justices in an unusual letter two weeks ago that the Arizona measures appeared to be lawful. But the letter disavowed the Trump administration’s position that the relevant section of the Voting Rights Act should not be widely used to keep states from enacting more restrictive voting procedures.

Much of the argument on Tuesday centered on that larger issue in the case, Brnovich v. Democratic National Committee, No. 19-1257, of what standard courts should apply to challenges under Section 2 of the Voting Rights Act. The court’s answer to that question could determine the fate of scores if not hundreds of laws addressing election rules in the coming years.

As Republican-controlled state legislatures increasingly seek to impose restrictive new voting rules, Democrats and civil rights groups are turning to the courts to argue that Republicans are trying to suppress the vote, thwart the will of the majority and deny equal access to minority voters and others who have been underrepresented at the polls.

“More voting restrictions have been enacted over the last decade than at any point since the end of Jim Crow,” Bruce V. Spiva, a lawyer for the Democratic National Committee, which is challenging the two Arizona measures, told the justices. “The last three months have seen an even greater uptick in proposed voting restrictions, many aimed squarely at the minority groups whose participation Congress intended to protect.”

Though the Voting Rights Act seeks to protect minority voting rights, as a practical matter litigation under it tends to proceed on partisan lines. When Justice Amy Coney Barrett asked a lawyer for the Arizona Republican Party why his client cared about whether votes cast at the wrong precinct should be counted, he gave a candid answer.

“Because it puts us at a competitive disadvantage relative to Democrats,” said the lawyer, Michael A. Carvin. “Politics is a zero-sum game, and every extra vote they get through unlawful interpretations of Section 2 hurts us.”

Jessica R. Amunson, a lawyer for Katie Hobbs, Arizona’s secretary of state, a Democrat, said electoral contests should not turn on voting procedures.

“Candidates and parties should be trying to win over voters on the basis of their ideas,” Ms. Amunson said, “not trying to remove voters from the electorate by imposing unjustified and discriminatory burdens.”

Section 2 took on additional prominence after the Supreme Court in 2013 effectively struck down the heart of the Voting Rights Act, its Section 5, which required prior federal approval of changes to voting procedures in parts of the country with a history of racial and other discrimination.

Until then, Section 2, which allows after-the-fact challenges, had mostly been used in redistricting cases, where the question was whether voting maps had unlawfully diluted minority voting power. Its role in addressing the denial of the right to vote itself has been subject to much less attention.

Over two hours of arguments by telephone, the justices struggled to identify a standard that would allow courts to distinguish lawful restrictions from improper ones.

The court did not seem receptive to a rigorous test proposed by Mr. Carvin, the lawyer for the Arizona Republican Party, who said that ordinary election regulations are not subject to challenges under Section 2. Most justices appeared to accept that regulations that place substantial burdens on minority voters could run afoul of the law.

But there was some dispute about what counted as substantial and what justifications states could offer for their restrictions. The court’s more conservative members seemed inclined to require significant disparities unconnected to socioeconomic conditions and to accept the need to combat even potential election fraud as a sufficient reason to impose restrictions on voting.

Justice Elena Kagan tested the limits of Mr. Carvin’s argument, asking whether much longer lines at polling places in minority neighborhoods could be challenged under the law. He said yes. He gave the same answer when asked about locating all polling places at country clubs far from minority neighborhoods.

But he said cutting back on Sunday voting, even if heavily relied on by Black voters, was lawful, as was restricting voting to business hours on Election Day.

Mark Brnovich, Arizona’s attorney general, a Republican, proposed a vaguer standard, saying that the disparate effect on minority voters must be substantial and caused by the challenged practice rather than some other factor.

Asked by Justice Kagan whether the four hypothetical restrictions she had posed to Mr. Carvin would survive under that test, Mr. Brnovich did not give a direct answer.

He did say that the number of ballots disqualified for having been cast in the wrong district was very small and that Arizona’s overall election system makes it easy to vote.

Ms. Amunson, the lawyer for Arizona’s secretary of state, urged the justices to strike down the challenged restrictions.

“Arizona already has a law prohibiting fraudulent ballot collection,” she said by way of example. “What this law does is it criminalizes neighbors helping neighbors deliver ballots with up to two years in jail.”

Justice Samuel A. Alito Jr. asked her a series of hypothetical questions about early voting, ballot forms and deadlines for mailed ballots. Ms. Amunson gave a general answer.

“You have to take a functional view of the political process and look to a holistic view of how it is actually affecting the voter on the ground,” she said.

Justice Alito appeared unsatisfied. “Well, those are a lot of words,” he said. “I really don’t understand what they mean.”

Several justices suggested that most of the standards proposed by the lawyers before them were quite similar. “The longer this argument goes on,” Justice Kagan said, “the less clear I am as to how the parties’ standards differ.”

Justice Stephen G. Breyer echoed the point. “Lots of the parties on both sides are pretty close on the standards,” he said.

Justices Kagan and Breyer, both members of the court’s liberal wing, may have been playing defense, hoping the court’s decision, expected by July, would leave Section 2 more or less unscathed.

But Justice Alito said he was wary of making “every voting rule vulnerable to attack under Section 2.”

“People who are poor and less well educated on balance probably will find it more difficult to comply with just about every voting rule than do people who are more affluent and have had the benefit of more education,” he said.

Justice Barrett appeared to agree. “All election rules,” she said, “are going to make it easier for some to vote than others.”

But Justice Brett M. Kavanaugh said he could think of two workable standards for applying the law. “One factor would be if you’re changing to a new rule that puts minorities in a worse position than they were under the old rule,” he said, “and a second factor would be whether a rule is commonplace in other states that do not have a similar history of racial discrimination.”

Last year, the United States Court of Appeals for the Ninth Circuit, in San Francisco, ruled that both Arizona restrictions violated Section 2 because they disproportionately disadvantaged minority voters.