Meanwhile, Bloomberg said he plans to take the subway on Monday, a sign that transit is coming back.

New York City students will also go back to school Monday, Bloomberg said. Some students will be bused to other locations if their schools have been damaged and cannot reopen.

Adding to concerns, a storm is forecast for the region this week.

"As we have this nor'easter coming ... we have to remain extremely vigilant about our neighbors," New York Sen. Kirsten Gillibrand said Sunday.

While many residents are seeking disaster relief help from federal and state officials, she said, some of the state's seniors may be afraid to leave their homes, even if they don't have heat. And they may not know what resources are available.

"What I'm most concerned about right now are the people we haven't met and we haven't seen," she said.