NEW YORK — With many residents left homeless after the devastation from last week’s storm, New York-area officials began focusing Sunday on another factor that might make the problems even worse: colder weather that is moving into the region.
In New York, 20,000 to 40,000 people, many of them residents of public housing, will have to find homes, Mayor Michael R. Bloomberg said Sunday. Earlier in the day, Bloomberg compared it to the situation after Hurricane Katrina in New Orleans but later seemed to temper his assessment after news that power had begun to flow in some of the hardest-hit regions.
Still, he said, at least 20,000 people live in housing where boilers and electrical circuits were severely damaged by the storm surge. Relocating them, he said, will be a daunting task.
‘‘We don’t have a lot of empty housing in this city,’’ he said at a press conference. ‘‘We are not going to let anybody go sleeping in the streets or go without blankets, but it’s a challenge, and we’re working on that as fast as we can.’’
Many residents in New Jersey, on Long Island, and in Connecticut face a similar problem.
The Federal Emergency Management Agency announced Sunday that it would begin providing transitional housing to those who could not return to their homes. As of Sunday morning, 164,000 residents of Connecticut, New Jersey, and New York had applied for aid, and the agency had approved more than $137 million in financial assistance.
Bloomberg called the cold the most pressing challenge in the recovery. The city has opened heating shelters and is passing out blankets to New Yorkers without electricity.
Temperatures throughout the region fell early Sunday into the 30s, and the National Weather Service issued a freeze watch on Sunday for parts of New Jersey, including the coast, where many residents remained without heat. Officials have urged them to head to shelters.
‘‘You can die from being cold,’’ Bloomberg said Sunday. ‘‘You can die from fires started from candles or stoves. Please go to the local disaster site.’’
Adding to the concerns, forecasters now say that a nor’easter could move in by midweek, hitting the already battered coastal areas with heavy winds and strong waves. Freezing temperatures are also expected.
Though the lights continued to flicker on, including in some hard-hit regions like the Rockaways, as of Sunday, more than 700,000 utility customers remained without power in New York state, including 404,000 on Long Island and 154,000 in New York City.
Nearly a million customers in New Jersey and 70,000 in Connecticut were also still without power. But restoring electric service is only the first step. When the storm surge flooded homes along the coast, the ocean water destroyed boilers and hot-water heaters.
Yet amid the despair, there has been an outpouring of good will. On Staten Island, in the Rockaways, and in other regions pummeled by Hurricane Sandy, thousands of people, including runners in Manhattan who had expected to compete in the New York City Marathon, which was canceled late last week, have pitched in to haul away fallen trees and distribute food and clothing.
The narrow streets of Midland Beach, one of the hardest hit areas on Staten Island, were buzzing with activity. Volunteers carried hoes, rakes, brooms, and shovels as they went door to door offering their labor.
Others circled the blocks in pickup trucks full of food, blankets, clothes, and cleaning supplies. Impromptu distribution centers, piled high with food and secondhand clothes, sprung up on every other corner.
On Sunday morning, runners dressed in orange New York Marathon gear overtook the Staten Island Ferry and headed to the storm-ravaged borough looking to help. They packed blankets, food, water, and flashlights in shoulder bags. Some planned to run to battered areas once the ferry docked.
Yet, it was not enough to solve some of the immense problems facing the region. There are continuing difficulties in delivering fuel. In New Jersey, Governor Chris Christie has declared a fuel emergency and imposed gasoline rationing in 12 counties.
On Sunday, gas lines seemed slightly shorter in some places, but many stations were still closed. Authorities have set up three fuel depots in New Jersey so doctors and nurses can get up to 15 gallons of gas to go to work.
Cuomo said that tankers and barges were on the way to help alleviate shortages. The Port Authority of New York and New Jersey announced that Port Elizabeth, N.J., reopened Sunday to receive its first shipment of cargo since it was closed by Hurricane Sandy. All other Port Authority seaports remained closed.
Monday’s commute could be complicated by the return of nearly a million children to school. About 96 percent of the city’s school buses are expected to be operating, and all but 65 schools should be open, Bloomberg said.