WASHINGTON — The House voted on Thursday to allow Puerto Ricans to decide the political future of the territory, the first time the chamber has committed to backing a binding process that could pave the way for Puerto Rico to become the nation’s 51st state or an independent country.

The measure, which has the support of the White House, has little chance of becoming law in the short term. It is all but certain to fall short of the 60 votes needed to break a filibuster in the Senate, where most Republicans are opposed, and there is little time left under this Congress before the G.O.P. takes control of the House in early January, likely burying the effort for at least the next Congress.

But the bipartisan vote — the bill passed 233 to 191 — was a symbolic statement by the House that Puerto Rico’s status as a colonial territory was both untenable and unwanted by many of its voters.

The legislation would establish a binding process for a referendum in Puerto Rico that would allow voters to choose among allowing the territory to become a state, an independent country or a sovereign government aligned with the United States. It would also lay out the processes for implementing the outcome of the vote and establish a campaign to educate voters about their options.

More than a decade after the House last weighed in on the status of Puerto Rico, it was the first time lawmakers voted to require the federal government both to honor the outcome of such a referendum and to ensure its implementation, aides said.

Sixteen Republicans joined 217 Democrats in approving the measure.

“Today’s historic vote is a key step toward ensuring that Puerto Rico’s future is one of its own choosing,” Speaker Nancy Pelosi, Democrat of California, said in a statement. “With the Puerto Rico Status Act, the Democratic House has proudly voted to tear down the vestiges of colonialism.”Puerto Rico has been an American territory since 1898, following the Spanish-American War.

Puerto Ricans often refer to the island as colonized twice, first by Spain and later by the United States. Puerto Rico’s 3.3 million residents are U.S. citizens but do not have voting representation in Congress and cannot vote in presidential elections. They also generally do not pay federal income tax on income earned in Puerto Rico and are not equally eligible for some federal programs.

Puerto Ricans have sought greater self-determination for decades, with the island’s territorial status deeply dividing its people. The three main political parties, which do not neatly align with Democrats and Republicans, are also divided over the question of status: The Puerto Rican Independence Party favors separating from the United States; the New Progressive Party favors statehood, and the Popular Democratic Party favors remaining a U.S. commonwealth.

The island’s status came under renewed scrutiny after Congress wrote a bankruptcy law named Promesa in 2016 that created an unelected federal oversight board to manage Puerto Rico’s bankrupt finances. Puerto Ricans, who refer to the unpopular board as “la junta,” have protested the board’s austerity measures and lack of accountability to people at the ballot box.

Puerto Rico has held six plebiscites on whether it should become a state, most recently in 2020, when 52 percent of voters on the island endorsed the move. None of the plebiscites has been binding, however, and turnout has often been low, amid boycotts by critics who support the status quo or independence.

Though the Republican Party platform, which has not been updated since 2016, supports statehood for Puerto Rico, Republicans in Congress have distanced themselves from that position, fearing that a Puerto Rican state could result in the election of more Democrats — a notion challenged by a recent strain of social conservatism within the island’s politics.

Congress is also unlikely to welcome as a state an island that has among the highest poverty levels in the United States and where most people’s primary language is Spanish.

Jenniffer González-Colón, the resident commissioner of Puerto Rico and its lone representative in Congress, backed a compromise measure among competing plans. A Republican, Ms. González-Colón is a member of the Puerto Rican political party that supports statehood, but acknowledged the “political realities in this Congress” had resulted in the compromise. Gov. Pedro A. Pierluisi, who is also a member of the statehood party and was present in the House for the vote, is a Democrat, underscoring the island’s complicated political allegiances.