Federal officials are considering spending more than $1 billion of the remaining $3.6 billion of rebuilding aid on disasters other than superstorm Sandy, money that New York and New Jersey are banking on to finish repairs to thousands of homes and complete major infrastructure projects.

The U.S. Department of Housing and Urban Development, which is in charge of distributing the aid, believes that spreading the funds around to disasters other than Sandy is required by federal law, according to people familiar with the matter. New York officials dispute that interpretation.

HUD officials recently briefed members of Congress on a proposal that would create a national resiliency competition to more widely distribute about $1 billion to $2 billion of the remaining Sandy aid to areas that have recently suffered disasters. It would be the first time HUD held a national competition for federal disaster money. The contest would reward projects that make communities more resilient against future disasters, according to people familiar with the plans.

Federal officials said they hope to have a decision by early May. "Our number one priority is to continue working with state and local officials to address the remaining unmet needs of those affected by natural disasters. In regards to any disaster funding, no determination has been made on programming or allocations of remaining funds," a HUD spokeswoman said.

The idea sets up the possibility that New York City, New York and New Jersey would have to compete with other states for the money. Other states are scrambling to make a case that they should receive a large share, said Staten Island Rep. Michael Grimm, a Republican whose district was hit hard by Sandy.