Hurricane Henri was due to crash into the north-eastern US coast on Sunday, as heavy rain caused flooding in some areas of New York and nearby cities.

Millions on New York’s Long Island and in southern New England were braced for flooding, toppled trees and extended power outages.

With the centre of the storm projected to pass just off the eastern tip of Long Island by midday, hurricane warnings extended from coastal Connecticut and Rhode Island to near the old whaling port of New Bedford, Massachusetts, and across the luxurious oceanfront estates of New York’s Hamptons to the summer getaway of Fire Island.

The first thunderstorms bringing what could be up to six inches (15cm) of rain arrived late on Saturday, and flash flooding began in some areas overnight. Bands of heavy rain overwhelmed storm drains and drivers ploughed through foot-deep water in a few spots in New York City, and Newark and Hoboken, New Jersey.

Tropical storm-intensity winds were expected to begin striking the coast at around 8am.

People in the projected path spent Saturday scrambling to stock up on groceries and fuel. Those close to the coast boarded up windows and, in some cases, evacuated.

Residents and visitors on Fire Island, a narrow strip of sandy villages barely above sea level off Long Island’s southern coast, were urged to evacuate. The last boats out left before 11pm on Saturday and officials warned there might be no way to reach people left behind.

The evacuation threw a wrench into Long Island resident Kristen Pavese’s planned Fire Island bachelorette party. Her group of 10 had intended to celebrate on Saturday night, but ended up leaving on the ferry just a day after arriving. They had planned to stay until Monday.

“I’m upset about it, but it’s the weather. It’s nothing I can control,” said Pavese. “I’ve been going to Fire Island for a long time, so I’m sort of familiar with this happening.”

Approaching severe weather on Saturday night also cut short a superstar-laden concert in Central Park. The show headlined by Bruce Springsteen, Paul Simon and Jennifer Hudson was meant to celebrate New York City’s recovery from the coronavirus. But officials asked concertgoers to leave the park during Barry Manilow’s set, amid the threat of lightning.

Governor Andrew Cuomo, who is to leave office on Monday after resigning over a sexual harassment scandal, pleaded with New York residents on Saturday to make last-minute preparations, warning that heavy rain, wind and storm surge from Henri could be as devastating as Superstorm Sandy in 2012.

“We have short notice. We’re talking about tomorrow,” Cuomo said. “So if you have to move, if you have to stock up, if you have to get to higher ground, it has to be today. Please.”

In Connecticut, Governor Ned Lamont warned residents they should prepare to “shelter in place” from Sunday afternoon through to at least Monday morning as the state braced for the first possible direct hit from a hurricane in decades. The Rhode Island governor, Dan McKee, issued a similar warning.

Major airports in the region remained open as the storm approached, though hundreds of Sunday’s flights were cancelled. Service on some branches of New York City’s commuter rail system was suspended through Sunday, as was Amtrak service between New York and Boston.

The White House said President Joe Biden discussed preparations with north-eastern governors and that the New York lieutenant governor, Kathy Hochul, who succeeds Cuomo on Tuesday, also participated.

Biden later began approving emergency declarations with Rhode Island.

New York has not had a direct hit from a powerful cyclone since Superstorm Sandy wreaked havoc in 2012. Some of the most important repairs from that storm have been completed, but many projects designed to protect against future storms remain unfinished.

With maximum sustained winds at 75mph, just above hurricane strength, Henri was moving north at 18mph as of Sunday morning. It was about 80 miles (125km) south-southeast of Montauk Point on the tip of Long Island.

Some gas stations from Cape Cod to Long Island sold out of fuel. The Southampton town supervisor, Jay Schneiderman, described a run on supplies such as batteries and flashlights as people were “starting to wake up”, and weather models showed the storm’s centre would run “smack on” Southampton.

Regardless of the exact landfall, broad impacts were expected across a large swath of the north-east, extending inland to Hartford, Connecticut, and Albany, New York, and eastward to Cape Cod, which is hosting tens of thousands of summer tourists.

Storm surge between 3 and 5 feet (1 to 1.5 metres) was possible in much of Long Island Sound all the way to Chatham, Massachusetts, and slightly less on Long Island’s Atlantic coast, the hurricane centre said. Flash flooding was possible in inland areas already saturated by recent rain.

In the Hamptons, the celebrity playground on Long Island’s east end, officials warned of dangerous rip currents and flooding that was likely to turn streets such as the mansion-lined Dune Road into lagoons.

“We have a lot of wealthy people. There’s no doubt that we do, but everybody pulls together in an emergency,” Schneiderman said. “So, you know, yeah, there are people hanging out on their yachts at the moment drinking martinis, but they’re also starting to talk about this storm and I’m sure they’re going to want to be helpful.”