Advancing a debate that harks back to the country’s earliest days, the House passed legislation Thursday to award the residents of the nation’s capital a full voting representative in Congress.

The bill, approved 241 to 177, faces an uncertain future, with passage in the Senate considered less likely. The White House also said last month that advisers to President Bush would recommend that he veto the bill on constitutional grounds.

For supporters, the House vote was a victory for democracy, potentially righting a historical wrong and ending a situation of “taxation without representation” for 600,000 residents of the District of Columbia.

“This vote fulfills a promise of our democracy,” Representative Nancy Pelosi of California, the House speaker, said in her floor speech. “It reflects what we stand for at home and preach around the world.”

For critics, the bill is an unconstitutional measure that could set off a cascade of other changes, including demands for senators for the district and voting representatives for territories.

Better solutions, they say, would be a constitutional amendment or for Washington to be ceded back to Maryland, so residents could vote for representatives and senators.

“The Constitution explicitly says that members of Congress can only be elected by people who live in states,” said Representative Lamar S. Smith, Republican of Texas. “Article I, Section 2 reads, quote, ‘The House of Representatives shall be composed of members chosen every second year by the people of the several states.’ ”

In a nod to political realities, the legislation also provides Utah, a heavily Republican state, with a fourth representative as an at-large member. The state had narrowly missed getting a new representative after the 2000 census.

The odd pairing is meant to balance the presumably Democratic representative that would come from the District of Columbia. But 22 Republicans supported the measure, which was co-sponsored by one of them, Representative Tom Davis of Virginia.

But opponents of the legislation argued that the Utah provision violates the “one man, one vote” principle laid out by the Supreme Court.

Currently, Washington and four territories — American Samoa, Guam, the Commonwealth of Puerto Rico and the United States Virgin Islands — have Congressional delegates who can vote in committees and on floor amendments but not on final consideration of bills.

The district’s delegate, Eleanor Holmes Norton, helped lead the fight for the legislation. Like several others on Thursday, she spoke of Washington residents who have fought and died in Iraq and previous wars.

“In their name and in good conscience, I ask the House today finally to give the residents of the District of Columbia the vote they have fought for for 206 years,” she said.

Much of the drama over the legislation in recent weeks has been in obscure parliamentary maneuvering. Last month, after initially appearing to be headed for easy passage, the measure was derailed by a Republican motion that sought to add an amendment that would have lifted the District of Columbia’s ban on semiautomatic weapons. In response, Democratic leaders quickly pulled the measure.

Before the vote Thursday, Democratic leaders reworked the legislation to thwart a similar Republican maneuver.

Senator Joseph I. Lieberman, the Connecticut independent who is chairman of the committee that would consider the bill in the Senate, promised Thursday to bring up the measure “as quickly as possible.” But Senator Mitch McConnell, Republican of Kentucky, the minority leader, has said he opposes the legislation.

Senator Orrin G. Hatch, Republican of Utah, whom supporters of the bill are looking to for help, said Thursday in a statement that he generally supported the effort to give Utah another seat but that he did not think the Senate would pass such a bill. Mr. Hatch also said he had concerns about the constitutionality of the at-large seat.

The district’s nonvoting status has its roots in events of 1783, when Congress was rousted from Philadelphia by an angry mob of war veterans seeking back pay. State officials declined to intervene, forcing members to flee, first to Princeton, N.J., and then to New York City.

The episode convinced the founding fathers that Congress could be safe only with the creation of a federal enclave, free from the influence of a particular state. As a result, the district was created without a direct representative in Congress.

The bill’s advancement through the House is the closest the district has come to having a member of Congress since a proposed constitutional amendment faltered in 1978.