Barack Obama, the US president, has declared a "major disaster" in New York state and freed up federal aid for those who lost homes or businesses, after "super storm" Sandy swept through the Eastern Seaboard.
At least 15 people were reported to have died in New York, after one of the biggest storms to ever hit the country made landfall on Monday night in New Jersey.
The storm, which dropped just below hurricane status before striking land, which has left 33 people dead across several US states. It had already killed more than 60 people in the Caribbean.
Heavy snows threatened mountainous regions inland, and huge population centres of Baltimore, Philadelphia and Washington have been affected.
Michael Bloomberg, the mayor of New York City, said in a news conference on Tuesday morning that the upcoming challenges facing the city in the coming days "are enormous".
"The most recent report states three quarters of a million New Yorkers are without power," he said.
"You should expect, given the extent of damage, power will be out for two or three days, maybe even longer than that."
Bloomberg went on to say public transport will remain closed until further notice, and schools and airports will also remain closed on Tuesday.
"While the worst of the storm has passed, conditions are still dangerous, and I cannot stress this enough," he said.
Many streets in New York City are filled with floodwater, with some subway tunnels breached and flying debris littering deserted pavements.
The city had closed down subway, bus and commuter train systems as of Sunday night.
More than eight million US homes and businesses were without power after Sandy tore down power lines, flooded electrical networks and sparked an explosion at a Consolidated Edison substation on Manhattan's East River.
About a quarter of New York City's homes and businesses were without power 15 hours after the storm roared ashore accompanied by a nearly 4.2-metre tidal surge that flooded empty subway and highway tunnels.
More than one million people in a dozen states were under orders to evacuate as the massive system plowed westward.
One disaster forecasting company predicted economic losses could ultimately reach $20bn, only half insured.
Trees were downed across the region, falling debris closed a major bridge in Boston, and floodwater and gusts of wind buffeted coastal towns such as Fairfield, Connecticut, home to many commuters into New York City, where police cruisers blocked access to the beaches.
Power and back-up generators failed at New York University hospital, and patients were being elsewhere for care.
The storm's wind field stretched from the Canadian border to South Carolina, and from West Virginia to an Atlantic Ocean point about halfway between the US and Bermuda, easily one of the largest ever seen.
The National Hurricane Centre said Sandy came ashore as a "post-tropical cyclone", meaning it still packed hurricane-force winds but lost the characteristics of a tropical storm. It had sustained winds of 129km per hour (kph), well above the threshold for hurricane intensity.
NYSE Euronext remained closed on Tuesday, the first time it has shut as a result of weather for two consecutive days since 1888.
The southern tip of Manhattan where Wall Street and the NYSE are located lost power on Monday after being buffetted by Sandy, the worst storm to hit New York since at least 1938.
The federal government in Washington was also closed, and so too were schools up and down the East Coast.
Con Edison, New York's electric utility, said it expected "record-size outages". The company said it would pre-emptively shut down transformers in some areas to prevent further damage.
Early on Tuesday morning, US power company Excelon Corp declared an alert at the 615MW Oyster Creek nuclear power reactor in New Jersey due to rising ocean water from Sandy, a spokesman at the US Nuclear Regulatory Commission (NRC) said.
An alert is the second lowest of the NRC's four emergency classifications.
The NRC spokesman said if the flood waters continued to rise, it could affect the reactor's service water pumps, which are used for shut-down cooling and to cool the spent-fuel pool.