WASHINGTON, June 21 (Reuters) — Democrats in the U.S. Senate this week will try to advance legislation setting new national election standards, seeking to counter voting-rights rollbacks that Republican legislatures are pursuing across the country.

Senate Democrats spent the weekend trying to finalize a bill that could win the support of all 50 Democrats and independents in the 100-member chamber, even as Republicans showed no signs of joining an effort that would expand voting by mail and change the way congressional districts are drawn in an effort to prevent them from being designed along partisan lines.

If the Democrats' effort sputters this week and no further negotiations succeed, it could allow new, restrictive voting rules in some Republican-led states to stand, unless they are struck down in court challenges.

But it also could embolden Democrats to try to scrap or modify the Senate's long-standing "filibuster" rule requiring 60 votes to advance most legislation. Such a move could leave Republicans powerless if the Senate's 48 Democrats and two independents stick together, given that Vice President Kamala Harris, also a Democrat, has the power to break 50-50 ties.

Senate Majority Leader Chuck Schumer has scheduled a procedural vote for Tuesday to let the Senate begin debating an election reform bill.

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"We are working to come up with an agreement to compromise with Joe Manchin," Schumer told reporters on Sunday.

Manchin, a moderate Democratic senator, opposes a broader bill passed by the Democratic-led U.S. House of Representatives in March, and offered his own election reform ideas last week.

But with Senate Republicans poised to withhold their support, Schumer is unlikely to get the 60 votes needed to begin debate on a bill.

The Democratic-led push for federal voting rights legislation comes as Republican legislatures in politically pivotal states such as Georgia, Florida and Iowa passed sweeping voting restrictions following former President Donald Trump's defeat last November and his unsubstantiated claims of widespread voter fraud.

Democrats and voting rights advocates have sued state officials over the new laws, saying they will disproportionately disenfranchise voters of color, who helped propel Democratic President Joe Biden to victory last November.

'Federal takeover'

Republican lawmakers on Sunday reiterated their strong opposition to Democrats' federal election proposals.

Sen. Lindsey Graham, interviewed on "Fox News Sunday," called the House bill "the biggest power grab in the history of the country," while Sen. Rob Portman denounced what he called "a federal takeover of our election system" from the states, in an interview with NBC's "Meet the Press."

If Schumer can win over all 50 of his senators, including Manchin, he will be able to take his argument to the country that Republicans alone stymied a voting reform debate in the aftermath of efforts by Trump to overturn his election loss.

The 2020 presidential election saw the largest total turnout in U.S. history, as states temporarily opened up voting procedures, such as extended hours for casting ballots in person and expanded opportunities for mail-in voting because of the coronavirus pandemic raging at the time.

Many Republicans are trying to roll back those provisions, citing the need to improve election security. Dozens of judges rejected lawsuits asserting voting irregularities, and election officials across the country have said last year's vote was safe and secure.

(Reporting by Richard Cowan and Susan Cornwell; Editing by Soyoung Kim and Peter Cooney)