The U.S. Energy Department said more than 160,000 customers in 10 states were still without power, but transit operations were resuming in New Jersey and New York was powering up, CNN reported.
New York Gov. Andrew Cuomo plans to ask the federal government for at least $30 billion in disaster aid to help New York City and other areas of the state recover from the storm, officials said.
Sandy left more than $50 billion in damage in the New York region, making it the country's costliest storm after Hurricane Katrina, which savaged the Gulf Coast in 2005, causing damages of $145 billion, The New York Times said.
Congressional delegations from other storm-ravaged states, including New Jersey, Pennsylvania, New Hampshire, Virginia, Maryland, North Carolina and Virginia, also are likely to seek federal assistance, the Times said.
New York authorities added two to Sandy's death count -- a 66-year-old man who appeared to have drowned in his home on Staten Island, and a 77-year-old man from Far Rockaway, in Queens, who died of injuries he suffered when he fell down a flight of stairs.
On Saurday in Baldwin Harbor on New York's Long Island, residents protested a Long Island Power Authority requirement that each home be inspected before power was restored.
Reacting to the uproar from residents and officials, the authority revoked its inspection order and said on its website Sunday it expected to restore power to 99 percent of its customers by the end of the day Tuesday. About 95,000 LIPA customers in three counties were without power.
Consolidated Edison said Sunday it had restored power to about 95 percent of the homes and businesses determined to be safe to receive electricity, the Times said. The utility said it expects to have 99 percent of customers able to receive power back online by Tuesday.
U.S. Secretary of Homeland Security Janet Napolitano, surveying hard-hit Staten Island Sunday, praised cleanup efforts so far, but said much more needed to be done.
"First things first. Food, shelter, clothing for people who need it, assistance with finding housing, getting life back to normal, or as normal as it can be under the circumstances," she said, identifying housing as the No. 1 issue.
In his weekly radio address Sunday, New York Mayor Michael Bloomberg outlined the city's relief and rebuilding efforts, pledging "to keep doing everything possible to get life back to normal in our city -- especially for those hit hardest by the storm."
In addition to power outages, officials in New York and a dozen counties in New Jersey are rationing gasoline.
Commuting was expected to be easier for New York and New Jersey residents Monday after transit service resumed at several key stops on the PATH rail system, governors of the two states said.
President Obama is scheduled to be in New York Thursday to view the recovery efforts and announce a rebuilding program for the region.