Speaker John A. Boehner, Republican of Ohio, brought the bill to the House floor 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 T. 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 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. 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 administration is pleased that Congress has taken action to ensure that FEMA continues to have the funds to cover flood insurance claims, including over 100,000 claims from Hurricane Sandy the agency has already received,” Clark Stevens, a White House spokesman, said in a statement. “We continue to urge Congress to take up and pass the full supplemental request submitted last year to ensure affected communities have the support they need for longer term recovery.”

Congress’s action 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 financing to help the region rebuild.

“I am optimistic and worried,” said Senator Charles E. Schumer, Democrat of New York. “Optimistic because there is pressure on the House to produce. Worried because I know how difficult it is to get things through the Congress.”