The governor’s move comes as President Obama is scheduled to appear on Thursday in the New York City area, where he is expected to view the recovery efforts and announce a rebuilding program for the region. On Sunday, the Homeland Security secretary, Janet Napolitano, toured Staten Island to view the response there.

It is clear that the effects of the storm are still being acutely felt. More than 125,000 customers were still without power on Sunday, including about 110,000 customers served by the Long Island Power Authority. Many gas stations remained closed, but the city’s introduction of odd-even gas rationing seemed to have shortened lines.

The storm-related death toll in New York City officially rose to 43, as a man who fell during the storm in his home in Queens succumbed to his injuries on Saturday. And transportation officials made more progress on shuttered lines and crossings. The Brooklyn-Battery Tunnel will reopen only for bus traffic on Monday, and more service will be restored on the Long Island Rail Road and PATH.

Mr. Cuomo’s request could be seen as a challenge to Mr. Obama to make good on his pledge, delivered during a high-profile visit to New Jersey, to provide federal support for the recovery effort. But it also could be seen as a test of the governor’s ability to extract billions of dollars of aid from Washington at a difficult time, with White House officials and Congressional leaders searching to find areas of government to cut to avert a Jan. 1 fiscal crisis.

It is far from certain whether Mr. Cuomo will get what he is looking for despite the president’s reassurances. The amount the governor is apparently seeking would exceed the roughly $12 billion in FEMA disaster aid currently available in Washington without action from Congress, where there is likely to be strong opposition to more spending.