WASHINGTON — Senate Democrats will try again next week to advance a voting rights measure, Senator Chuck Schumer, the majority leader, announced on Thursday, though Republicans are expected to maintain their filibuster against the legislation backed by all Democrats.

In a letter laying out the coming agenda for the Senate, Mr. Schumer, Democrat of New York, said he would schedule a vote for next Wednesday to open debate on voting rights legislation that he and fellow Democrats say is needed to offset new restrictions being imposed by Republican-controlled state legislatures around the nation.

“We cannot allow conservative-controlled states to double down on their regressive and subversive voting bills,” Mr. Schumer said in the letter. “The Freedom to Vote Act is the legislation that will right the ship of our democracy and establish common sense national standards to give fair access to our democracy to all Americans.”

His decision intensifies pressure on Senator Joe Manchin III, Democrat of West Virginia, who had initially been his party’s lone holdout on a sweeping voting rights measure passed by the House. Mr. Manchin helped draft a compromise version that he said he hoped could draw bipartisan backing, and sought time to win over Republicans to support it, but there is little evidence that any G.O.P. senators have embraced the alternative.

In the 50-50 Senate, it would take 10 Republicans joining every Democrat to muster the 60 votes needed to break a filibuster of any voting rights bill and allow it to be considered.

Mr. Manchin’s compromise narrowed the objectives of the legislation, which would require states to allow a minimum of 15 days of early voting, ensure that all voters could request to vote by mail and make Election Day a national holiday, among other provisions. It would also establish requirements for voter identification, but less onerous ones than sought by Republicans.

Despite Mr. Manchin’s outreach, there has been little sign of movement among Republicans who have been steadfast in their opposition to the Democratic voting push, calling it an attempt to federalize state elections and grab an advantage for the Democratic Party. Their blockade of the voting rights bill has spurred calls to eliminate or change the filibuster rules, but Mr. Manchin has resisted those efforts.

Some Democrats who have been agitating for such changes have held out hope that when Mr. Manchin saw that Republicans were unwilling to support even his compromise measure, he would drop his opposition to altering the rules, despite his repeated vows that he never would.

In his letter, Mr. Schumer said that Democrats would also continue their internal negotiations to come up with a final version of a sweeping social safety net bill that has been slowed by differences between progressives and moderates over its cost and contents. He warned that lawmakers would need to make concessions to get a final measure.

“To pass meaningful legislation, we must put aside our differences and find the common ground within our party,” Mr. Schumer said. “As with any bill of such historic proportions, not every member will get everything he or she wants.”