WASHINGTON — The House of Representatives has overwhelmingly approved legislation that would allow the use of federal money to rebuild churches and synagogues damaged by Hurricane Sandy, despite concern that such aid could violate the doctrine of separation of church and state.

The bill, approved last week by a vote of 354 to 72, had support from Roman Catholic and Jewish organizations. It was opposed by 66 Democrats and 6 Republicans.

The prospects for the bill in the Senate are uncertain. Senator Kirsten E. Gillibrand, Democrat of New York, said Monday that she supported the measure and was working to secure its passage in the Senate. She noted that religious institutions like St. Francis de Sales Catholic Church in Belle Harbor, Queens, had provided aid to many storm victims.

Scores of churches, synagogues and other houses of worship were damaged — along with homes, schools, stores and roads — when the hurricane battered the Northeast in late October. Congress has provided $60 billion to finance recovery efforts.