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The measure is the first, and least controversial, portion of a much larger aid package sought by the affected states to help homeowners and local governments recover costs associated with the storm. The House has pledged to take up the balance of the aid package on Jan. 15.

The insurance measure passed 354 to 67 with overwhelming bipartisan support. It now goes to the Senate, where it is expected to pass later on Friday.

The bill was brought to the floor by Speaker John A. Boehner, a Republican from Ohio, after he drew criticism from Democrats and Republicans alike for adjourning the previous Congress earlier this week without taking up a $60.4 billion aid bill that the Senate had passed to finance recovery efforts in the hurricane-battered states. Among those most critical of Mr. Boehner were several leading Republicans, including Representative Peter King of Long Island, who is a senior member of Congress, and Gov. Chris Christie of New Jersey, who is a possible presidential contender in 2016.

The bill adopted by the House on Friday would give the National Flood Insurance Program the authority to borrow $9.7 billion to fill claims stemming from damage caused by Hurricane Sandy and other disasters. To date, the program has covered 140,000 storm-related claims, totaling about $1.7 billion.

The Federal Emergency Management Agency, which administers the flood insurance program, recently notified Congress that it would run out of money within the next week to cover claims filed by individuals.

The action by the House did not fully mollify lawmakers from New York, New Jersey, Connecticut and other states struck by the storm. Some officials continued to criticize the chamber's leadership for failing to act more quickly on the larger aid package, saying it provided the necessary funding to help the region rebuild.

The overall measure would cover an array of needs. It would provide money to help homeowners and small-business owners rebuild; to repair bridges, tunnels and transportation systems; to reimburse local governments for overtime costs of police, fire and other emergency services; and to replenish shorelines. It also would finance an assortment of longer-term projects that would help the regions brace for future storms.

In the debate leading up to Friday's vote, several lawmakers said it had taken too long for Congress to provide federal aid to the region, and urged the speaker to make good on his pledge to bring the $51 billion aid package to the floor later this month.

"We have been waiting for 11 weeks," said Representative Carolyn Maloney, a Democrat from New York City. "It is long overdue."

Representative Frank Pallone, a Democrat from New Jersey, was more critical. "This action by the Republican leadership is too little too late," he said.

Representative Nita Lowey, a Democrat from Westchester, called the $9.7 billion measure inadequate. "This bill is not enough," she said. "We don't need a piecemeal approach."

And Representative Jerrold Nadler, a Democrat from New York City, said the vote on Friday did "not excuse the callous action of the House the other night" when Mr. Boehner removed the larger aid package from the legislative calendar as previous Congress was rushing to conclude its business.