WASHINGTON, June 22 (Reuters) - Republicans in the narrowly divided U.S. Senate on Tuesday blocked an election reform bill considered a top priority by Democrats seeking to offset a wave of laws passed by Republican-led state legislatures that impose new limits on voting.

The 50-50 party-line vote fell short of the 60-vote threshold to advance most legislation in the Senate, sparking new calls by some Democrats to rethink that rule, known as the filibuster.

Republicans argued that the bill infringed on states' rights to set voting policy.

But Democrats vowed to fight on, with Senate Majority Leader Chuck Schumer saying: "In the fight for voting rights, this vote was the starting gun, not the finish line."

Vice President Kamala Harris - who presided over the Senate during the vote - called the effort critical.

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"This is about the American people's right to vote unfettered. It is about their access to the right to vote in a meaningful way, because nobody is debating, I don't believe, whether all Americans have the right to vote," she told reporters after the vote.

Republican state legislators justify their new voting laws by citing former President Donald Trump's continued false claims that his November election defeat was the result of widespread fraud. Those claims were rejected by multiple courts, state election authorities and Trump's own administration.

Democrats control Congress by the narrowest of margins and are highly focused on the risk of losing that majority in the 2022 midterm elections.

They say the Republican state bills, which include measures like Georgia's ban on providing food or water to voters in long lines and a Florida measure giving more power to partisan election observers are aimed at depressing turnout by people of color and young voters.

Democrats' goals include expanding early voting in elections for president and Congress, making it easier to vote by mail and ensuring that certain campaign contributions are more transparent. Their bills also aim to remove partisanship from the once-a-decade drawing of congressional districts.

Republicans argue the U.S. Constitution gives states the power to set their own voting practices. But the Constitution also allows Washington to alter those rules, and Democrats argue they are only setting minimum standards for states.

Senate Republican leader Mitch McConnell said before the vote that the legislation "would let Democrats take a red pen to election laws in each of the 50 states."

“Democrats want unaccountable bureaucrats in Washington to run our elections in Florida,” Republican Senator Marco Rubio said in a statement. “Not only is that unconstitutional, it is reckless. Florida election laws strike a fair balance between accessibility and security."

Democrats mull next moves

Reuters/Ipsos polling shows that Americans generally want to expand access to voting and many oppose the more restrictive measures being advanced in Republican-controlled state legislatures.

A survey conducted from June 11-17 showed that 59% of adults opposed reducing early voting hours, while 25% supported doing so.

Moderate Democratic Senator Joe Manchin had pushed for a bipartisan deal, even offering an alternative version of the bill that was not as far-reaching. But he failed to persuade a single Republican to open debate on the measure.

Anticipating failure in Tuesday's vote, some Democrats were already discussing alternative strategies for reining in the Republican efforts that reverse some of the 2020 election's expanded access for casting ballots.

Democratic House Majority Leader Steny Hoyer told reporters the likely Senate outcome "will be a dramatic evidence of why the filibuster needs to be modified."

Democratic Senator Debbie Stabenow alluded to possible legal action against Republican-led statutes, saying: "We have an attorney general and a (Justice Department) Civil Rights Division and a commitment from the president of the United States. And we will continue on in every way we can."

But the courts may not provide an easy win.

The conservative-majority Supreme Court in recent years has made it more difficult to challenge both voting restrictions and the drawing of legislative districts.

In 2013, it gutted a key section of the Voting Rights Act that protects minority voters and in 2019 rejected efforts to rein in electoral map manipulation by politicians aimed at entrenching one party in power, a practice known as gerrymandering. The court in coming days could further weaken the Voting Rights Act in a ruling on voting restrictions in Arizona.

(Reporting by Richard Cowan, Chris Kahn, Doina Chiacu and David Morgan; Editing by Scott Malone and Peter Cooney)