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The aid package passed 241 to 180, with 49 Republicans joining 192 Democrats to approve it. It now goes to the Senate, where it is expected to pass. President Obama has expressed support for the measure.

The $50.7 billion — along with a nearly $10 billion aid package that Congress approved about a week ago — seeks to provide for the huge needs that have arisen since the hurricane struck more than two months ago in New York, New Jersey, Connecticut and other states.

The emergency aid measure would help homeowners whose homes have been damaged or destroyed, provide assistance to business owners who experienced losses as well as reinforce shorelines, repair subway and commuter rail systems, fix bridges and tunnels, and reimburse local governments for emergency expenditures.

Though the package does not cover the entire $82 billion in damage identified by the governors of New York, New Jersey and Connecticut, leaders from the storm-ravaged region expressed relief over the action in the Republican-controlled House, where storm aid had become ensnared in the larger debate over spending and deficits.

Representative Peter T. King, a Republican from Long Island who helped press his party's leadership into holding the vote, hailed the package's passage as a victory for storm victims but expressed disappointment over the House's failure to act earlier.

"It is unfortunate that we had to fight so hard to be treated the same as every other state has been treated," he said.

Senator Charles E. Schumer, the New York Democrat who is part of the chamber's leadership, said he would urge the Senate to approve the House bill even though he believed it fell short of what the Senate approved last year. "It is certainly close enough," he said, comparing the bills.

The developments in the House settle, at least for now, an issue that had become an embarrassment for the chamber's Republican leadership and had pit Northeastern Republicans eager to help their constituents against fiscal conservatives bent on taming the nation's deficits.

The vote was scheduled over a week ago by Speaker John A. Boehner, Republican of Ohio, after he came under intense criticism for concluding the business of the previous Congress without taking up a $60.4 billion hurricane-aid bill that the Senate had approved.

His critics included influential Republicans in and out of Congress, including Mr. King and Gov. Chris Christie of New Jersey.

In a statement, Mr. Christie joined with Gov. Andrew M. Cuomo of New York and Dannel P. Malloy of Connecticut, both Democrats, to express gratitude to the Congress for providing the relief to hurricane victims.

The total $50.7 billion package was presented on the floor in a carefully structured legislative approach that reflected the political sensitivities surrounding the issue. House leaders first offered a spartan $17 billion bill and then a $33.7 billion amendment that was written by New Jersey and New York Republicans. The approach allowed House conservatives to vote for some of the assistance while lowering the total cost. The bulk of the money, contained in the amendment, ultimately needed Democratic votes to be tacked onto the final package and then passed.

In the debate leading up to passage of the aid package, Representative Carolyn Maloney, a Democrat from New York, argued that House should have acted sooner. "Residents have been suffering for two-and-a-half months," she said. "We need the aid. We need it now."

As the debate unfolded, lawmakers from the region found themselves on the defensive at times, forced to beat back a barrage of amendments that sought to cut items out of the overall package or that demanded cuts in other programs to pay for the package.

The most controversial of the amendments was offered by a group of conservative lawmakers who sought to pay for the aid package with across-the-board spending cuts to a variety of programs in the 2013 federal budget.

Critics called the amendment a poison pill, given that it would almost certainly doom the overall package's prospects of passage in the Democrat-controlled Senate. But the amendment's backers insisted that it was merely meant to clamp down on runaway spending and deficits.

"This amendment is not about offering a poison pill," said Representative Mick Mulvaney, a Republican from South Carolina and the amendment's author. "I want the money to go where it needs to go."

The amendment was defeated 258 to 162; 70 Republicans joined 188 Democrats to beat it back.