WASHINGTON — Stymied by Republicans on voting rights legislation, Senator Chuck Schumer on Monday gave the clearest sign yet that he would try to force a fundamental change in Senate rules if needed to enact federal laws to offset voting restrictions being imposed by Republican-led legislatures around the country.

In a letter to colleagues, Mr. Schumer, the New York Democrat and majority leader, said that the Senate would take up stalled voting rights legislation as early as the first week of January and that if Republicans continued to filibuster, the Senate would “consider changes to any rules which prevent us from debating and reaching final conclusion on important legislation.”

But it is not clear how far Democrats will be willing or able to go in working around the 60-vote requirement for most legislation and finding a way to pass voting rights legislation with a simple majority. While several formerly reluctant senators have in recent weeks endorsed rules change for voting issues, at least two Democratic senators — Joe Manchin III of West Virginia and Kyrsten Sinema of Arizona — have resisted.

Alarmed by state laws being enacted in the aftermath of the 2020 election that seem aimed at making it more difficult for people, particularly minorities, to vote, Democrats have tried repeatedly this year to set federal standards for early and mail-in voting and curb partisan gerrymandering, among other provisions. But they have been consistently thwarted by a Republican blockade.

To this point, Democrats have not pressed the issue. But Mr. Schumer’s new stance shows that he is ready to take the next step and start a rules fight on the Senate floor though he has so far lacked the 50 Democratic votes needed to force through a change over Republican opposition.

Mr. Schumer’s move seems intended to change the dynamic of the debate and put new pressure on his colleagues to back a change. Mr. Schumer’s frustration boiled over in his letter, saying it was unfair to let states set new rules through partisan majority votes while Republicans were preventing the Senate from doing the same.

“I would ask you to consider this question,” he wrote. “If the right to vote is the cornerstone of our democracy, then how can we in good conscience allow for a situation in which the Republican Party can debate and pass voter suppression laws at the state level with only a simple majority vote, but not allow the United States Senate to do the same?”

Mr. Schumer has in the past said mainly that “all options are on the table” when it comes to pressing voting rights legislation, refraining from a direct threat on Senate rules.

A group of more moderate Senate Democrats have been engaged in negotiations on rules changes with Mr. Manchin and Ms. Sinema and have reported some progress but no breakthrough. While Mr. Manchin on Sunday shattered Democratic plans to push forward on a sweeping social policy and climate change bill, he opened the door a crack to potential changes in Senate rules.

“If you can make the Senate work better, the rules are something we’ve changed over the years; 232 years, there’s been rule changes,” Mr. Manchin said Sunday on Fox News. But he also suggested that he might be interested in more modest changes than Mr. Schumer and others are contemplating, saying he would continue to support the 60-vote, supermajority threshold to overcome a filibuster.

Ms. Sinema has also drawn a line against partisan changes in the rules, but Democrats say they believe she would not want to be the lone holdout if Mr. Manchin were persuaded to relent on the legislative filibuster.

Democrats knowledgeable about the internal deliberations say that many possible changes are under consideration, including weakening the filibuster against the preliminary “motion to proceed” to bring legislation to the floor for consideration. But in a more significant move, Democrats say they are also discussing a change that would clear the way for final action on a bill through a simple majority vote after guaranteeing opponents the opportunity to alter the legislation through a significant number of amendments.

Instituting such a change would require the support of all 50 Democrats and the vote of Vice President Kamala Harris presiding to break a tie in the 50-50 Senate.

Democrats say such a filibuster “carve out” would apply only to issues grounded in constitutional rights such as voting, but Republicans and others say it would inevitably be extended to other legislation, diminishing the overall power of the filibuster.

The Democratic voting rights and rules change push would meet universal resistance from Republicans. Senator Mitch McConnell, the Kentucky Republican and minority leader, last week accused Democrats of “rattling swords about changing the structure of the Senate” and commended Mr. Manchin for opposing it.

“Changing the structure of the Senate in order to achieve a partisan advantage is a mistake for the Senate and a mistake for our country,” he said.

Once used rarely, the filibuster has become a routine aspect of the Senate in recent decades and virtually all legislation now has to clear a 60-vote hurdle just to be debated on the floor, severely limiting what business can be taken up.

Outraged over Republicans blocking President Barack Obama’s judicial nominees through regular filibusters, Democrats in 2013 took the procedural steps to allow most nominees to be confirmed with a simple majority vote. Republicans countered in 2017 by extending that rule to Supreme Court nominees, enabling President Donald Trump to install three high court justices.

In a statement in the letter directed at Mr. Manchin, Mr. Schumer noted that Senator Robert C. Byrd, a Senate stalwart whose seat Mr. Manchin occupies, said in 1979 that sometimes Senate rules that seemed appropriate “must be changed to reflect changed circumstance.”

“I believe our constituents deserve to know which senators choose to hide behind ill-conceived and abused rules and which senators prefer to restore Senate floor procedures to better align with the founders’ intentions,” Mr. Schumer wrote.