WASHINGTON — The House, dismissing concern for the rising cost, approved a $36.5 billion aid package on Thursday that would provide hurricane and wildfire relief funding while bailing out the financially troubled National Flood Insurance Program.

The aid package would also help Puerto Rico’s financially beleaguered government avoid running out of cash in the wake of Hurricane Maria. Conditions there remain dire, with most of the island still without power three weeks after the storm hit.

The House approved the bill 353 to 69, with all of the no votes coming from Republicans.

The disaster package, now awaiting consideration in the Senate, would be the second installment of aid money that Congress has approved in response to this year’s hurricanes, after a $15.3 billion relief measure in September. With the tab now more than $50 billion, lawmakers warn that much more money will still be needed. Lawmakers from Texas and Florida have already outlined expansive requests, adding up to tens of billions of dollars in total. And the United States Virgin Islands delegate to the House, Stacey Plaskett, a Democrat, complained that the package lacked aid needed by her devastated territory.

“I know people are concerned that not every state’s need is met, but this is, I think, a good step in the right direction,” said Representative Rodney Frelinghuysen, Republican of New Jersey and chairman of the House Appropriations Committee, who urged his colleagues to vote for the bill “so we can get this money out the door as quickly as possible.”