Tens of thousands of people displaced by super-storm Sandy could soon need housing as cold weather closes in.
New York City mayor Michael Bloomberg put the figure at 30,000 - 40,000 people.
Federal agencies are looking for flats and hotel rooms in order to get people out of shelters, Homeland Security Secretary Janet Napolitano said.
At least 106 deaths in the United States, including 40 in New York City, have been blamed on Sandy, which struck on 29 October, the BBC reports.
The storm had already caused 69 deaths in the Caribbean before making landfall at New Jersey on the east coast of the US at the beginning of last week.
Below-freezing temperatures are expected on Monday.
New York State governor Andrew Cuomo said on Sunday that homes without heat would become uninhabitable as temperatures fell and residents who had so far refused to leave their houses would have no option.
Mr Cuomo said there would be increasing pressure on public transport on Monday as more people returned to work and the schools re-opened.
Fuel shortages were easing, but he urged New Yorkers not to hoard petrol, saying more supplies were on their way.
New York City has opened warming shelters in areas without power and handed out blankets to residents who insisted on staying in homes without power. However, Mr Bloomberg urged those without heating to leave their homes if necessary.
About 730,000 people in New York state still do not have electricity, including more than 130,000 in New York City, the governor said. Nearly 1 million people in the neighbouring state of New Jersey remain without power.
Meanwhile, Hundreds of runners who had been planning to take part in the New York marathon - cancelled by Mr Bloomberg on Friday - joined impromptu runs to raise funds or deliver aid.
Haiti appeals for aid
The Haitian government has appealed for humanitarian assistance from other governments and international organisations in the wake of the storm.
Aid agencies in Haiti have voiced concerns about the damage caused by Sandy which destroyed crops and left thousands of people homeless when it was hurricane strength.
There are also fears about the spread of cholera in flooded areas.