Bloomberg said there was just no telling when power and transit would be back, but estimated some bus service would be restored by Tuesday afternoon.
"Clearly the challenges our city faces in the coming days are enormous," he said.
Water lapped over the seawall in Battery Park City, flooding rail yards, subway tracks, tunnels and roads. Rescue workers floated bright orange rafts down flooded downtown streets, while police officers rolled slowly down the street with loudspeakers telling people to go home.
In Queens, nearly 200 firefighters tried to contain an enormous blaze that consumed more than 80 homes in the Breezy Point neighborhood. They had to use a boat to make rescues and climbed an awning to reach about 25 trapped people, fire officials said.
Officials weren't immediately able to pin down the cause of the blaze, and Bloomberg said no deaths had been reported there.
On Staten Island, a tanker ship wound up beached on the shore.
Water surged into two major commuter tunnels - the Brooklyn Battery and the Queens Midtown. Water coursed into one of the Long Island Rail Road's East River tunnels, the railroad's West Side yards had to be evacuated. At least 40 LIRR stations had no power Tuesday.
The rains and howling winds left a crane hanging off a luxury high-rise in midtown Manhattan, causing the evacuation of hundreds from a posh hotel and other buildings. Inspectors were climbing 74 flights of stairs to examine the crane hanging from the $1.5 billion building.
After a backup generator failed, New York University's Tisch Hospital began evacuating more than 200 patients to other facilities, including 20 babies from neonatal intensive care, some of them on respirators operating on battery power.
In Schwartz's Brooklyn neighborhood of Red Hook, residents who ignored a mandatory evacuation order awoke to debris-strewn streets and a continued blackout. About 2 inches of mucky dirt and leaves covered streets crisscrossed by downed power lines after water sloshed 12 blocks inland.