State governor Kathy Hochul declared a state of emergency over the “extreme rainfall”, after more than five inches of rain fell in some areas overnight.
As much as 7 inches more was expected throughout the day, she said.
“This is a dangerous, life-threatening storm," Ms Hochul said in an interview with TV station NY1. “Count on this for the next 20 hours."
Although by midday (5pm BST), there was a break in the clouds, Mayor Eric Adams urged people to stay put if possible.
“It is not over, and I don't want these gaps in heavy rain to give the appearance that it is over," he said at a news briefing. Officials said there were no fatalities yet recorded as a result of the flooding.
Photos and video posted on social media showed water pouring into subway stations and basements, and reaching the top of cars’ wheels in parts of Brooklyn and elsewhere.
— NYScanner (@nyscanner) September 29, 2023
The city’s Metropolitan Transportation Authority, which runs subway and commuter rail lines, urged residents to stay home if they could.
Almost every subway line was at least partly suspended, rerouted or running with delays amid the flooding.
Traffic was also at a standstill, with water above cars' tyres, on a stretch of FDR Drive - a major artery along the east side of Manhattan. Some drivers abandoned their vehicles.
Priscilla Fontallio said she had been stranded in her car, which was on a section of the highway that was not flooded but was not moving, for three hours.
“Never seen anything like this in my life," she told the Associated Press.
In Brooklyn, residents emerged from their homes to survey the damage and begin draining the water that reached the top of many basements doors.
Some people arranged milk crates and wooden boards to cross the flooded pavements, with water close to waist-deep in the middle of some streets.
High school student Malachi Clark said he was unsure how to proceed as he tried to get home to Brooklyn's Bedford-Stuyvesant neighbourhood.
“When it stops the buses, you know it's bad," he said.
Flooding also was reported in surrounding areas, including Hoboken, New Jersey.
The US National Weather Service said in an advisory notice: “Move to higher ground now. Act quickly to protect your life.”
The state of emergency declared by Ms Hochul affects New York City, Long Island, and the Hudson Valley.
“Please take steps to stay safe and remember to never attempt to travel on flooded roads," she said in a message posted on the X, formerly Twitter.
Some 18 million people in the New York metropolitan area and in other major cities along the East Coast were under flood warnings, watches and advisories from the weather service.