NEW YORK — Frustration — and in some cases fear — mounted in New York City on Thursday, three days after Superstorm Sandy. Traffic backed up for miles at bridges, large crowds waited impatiently for buses into Manhattan, and tempers flared in gas lines.

Mayor Michael Bloomberg said the city would send bottled water and ready-to-eat meals into the hardest-hit neighborhoods through the weekend, but some New Yorkers grew dispirited after days without power, water and heat and decided to get out.

“It’s dirty, and it’s getting a little crazy down there,” said Michael Tomeo, who boarded a bus to Philadelphia with his 4-year-old son. “It just feels like you wouldn’t want to be out at night. Everything’s pitch dark. I’m tired of it, big-time.”

Rima Finzi-Strauss decided to take the bus to Washington. When the power went out Monday night in her apartment building on the Lower East Side of Manhattan, it also disabled the electric locks on the front door, she said.

“We had three guys sitting out in the lobby last night with candlelight, and very threatening folks were passing by in the pitch black,” she said. “And everyone’s leaving. That makes it worse.”

The mounting despair came even as the subways began rolling again after a three-day shutdown. Service was restored to most of the city, but not the most stricken parts of Manhattan and Brooklyn, where the tunnels were flooded.

Bridges into the city were open, but police enforced a carpooling rule and peered into windows to make sure each car had at least three people. The rule was meant to ease congestion but appeared to worsen it. Traffic jams stretched for miles, and drivers who made it into the city reported that some people got out of their cars to argue with police.

Rosemarie Zurlo said she planned to leave Manhattan for her sister’s place in Brooklyn because her own apartment was freezing, “but I’ll never be able to come back here because I don’t have three people to put in my car.”

With only partial subway service, lines at bus stops swelled. More than 1,000 people packed the sidewalk outside an arena in Brooklyn, waiting for buses to Manhattan. Nearby, hundreds of people massed on a sidewalk.

When a bus pulled up, passengers rushed the door. A transit worker banged on a bus window, yelled at people inside, and then yelled at people in the line.

With the electricity out and gasoline supplies scarce, many gas stations across the New York area remained closed, and stations that were open drew long lines of cars that spilled out onto roads.

At a station near Coney Island, almost 100 cars lined up, and people shouted and honked, and a station employee said he had been spit on and had coffee thrown at him.

In a Brooklyn neighborhood, a station had pumps wrapped in police tape and a “NO GAS” sign, but cars waited because of a rumor that gas was coming.

“I’ve been stranded here for five days,” said Stuart Zager, who is from Brooklyn and was trying to get to his place in Delray Beach, Fla. “I’m afraid to get on the Jersey Turnpike. On half a tank, I’ll never make it.”

The worst was over at least for public transportation. The Long Island Rail Road and Metro-North were running commuter trains again, though service was limited. New Jersey Transit had no rail service but most of its buses were back, and Amtrak said it would run trains between New York and Boston Friday for the first time since the storm hit.

The storm killed at least 90 people in the U.S. New York City raised its death toll on Thursday to 38, including two Staten Island boys, 2 and 4, swept from their mother’s arms by the floodwaters.

In New Jersey, many people were allowed back into their neighborhoods Thursday for the first time since Sandy ravaged the coastline. Some found minor damage, others total destruction.

The storm cut off barrier islands, smashed homes, wrecked boardwalks and hurled amusement park rides into the sea. Atlantic City, on a barrier island, remained under mandatory evacuation.

More than 4.1 million homes and businesses, including about 650,000 in New York and its northern suburbs, were still without power. Consolidated Edison, the power company serving New York, said electricity should be restored by Saturday to customers in Manhattan and to homes and offices served by underground power lines in Brooklyn.

In darkened neighborhoods, people walked around with miner’s lamps on their foreheads and bicycle lights clipped to shoulder bags and, in at least one case, to a dog’s collar. A Manhattan handyman opened a fire hydrant so people could collect water to flush toilets.

“You can clearly tell at the office, or even walking down the street, who has power and who doesn’t,” said Jordan Spiro, who lives in the blackout zone. “New Yorkers may not be known as the friendliest bunch, but take away their ability to shower and communicate and you’ll see how disgruntled they can get.”

Some public officials expressed exasperation at the relief effort.

James Molinaro, president of the borough of Staten Island, suggested that people not donate money to the American Red Cross because the Red Cross “is nowhere to be found.”

“We have hundreds of people in shelters throughout Staten Island,” he said. “Many of them, when the shelters close, have nowhere to go because their homes are destroyed. These are not homeless people. They’re homeless now.”

Josh Lockwood, the Red Cross’ regional chief executive, said 10 trucks began arriving to Staten Island on Thursday morning and a kitchen was set up to distribute meals. Lockwood defended the agency, saying relief workers were stretched thin.

“We’re talking about a disaster where we’ve had shelters set up from Virginia to Indiana to the state Maine, so there’s just this tremendous response,” he said. “So I would say no one organization is going to be able to address the needs of all these folks by themselves.”

In Manhattan’s Chelsea neighborhood, Mary Wilson, 75, was buying water from a convenience store that was open but had no power. She said she had been without running water or electricity for three days, and lived on the 19th floor.

She walked downstairs Thursday for the first time because she ran out of bottled water and felt she was going to faint. She said she met people on the stairs who helped her down.

“I did a lot of praying: ‘Help me to get to the main floor.’ Now I’ve got to pray to get to the top,” she said. “I said, ‘I’ll go down today or they’ll find me dead.”’