UNION, N.J. — Widespread gas shortages stirred fears among residents and disrupted some rescue and emergency services on Thursday as the New York region struggled to return to a semblance of normalcy after being ravaged by Hurricane Sandy.

Tiny increments of progress — some subway and bus lines were back in service — were overshadowed by new estimates of the storm’s financial cost, struggles to restore power, and by the discovery of more bodies in flooded communities.

The lines of cars waiting for gas at a Sunoco here ran in three directions: a mile-long line up the Garden State Parkway, a half-mile line along Vauxhall Road, and another, including a fleet of mail trucks that needed to refuel before resuming their rounds, snaking through a back entrance. The scene was being replayed across the state as drivers waited in lines that ran hundreds of vehicles deep, requiring state troopers and local police to protect against exploding tempers.

“I’ve been pumping gas for 36 hours, I pumped 17,000 gallons,” said Abhishek Soni, the owner of an Exxon in Montclair, where disputes on the line Wednesday night had become so heated that Mr. Soni called the police and turned off the pumps for 45 minutes to restore calm. “My nose, my mouth is bleeding from the fumes. The fighting just makes it worse.”

Robert Stolarik for The New York Times

A gas station in Williamsburg, Brooklyn, had long lines on Thursday, and police officers to keep the peace. Officials said the fuel shortage would thin the taxi fleet. More Photos »

Four days after Hurricane Sandy, the effort to secure enough gas for the region moved to the forefront of recovery work. The problems affected even New York City, where the Taxi Commission warned that the suddenly indispensable fleet of yellow cabs would thin significantly Friday because of the fuel shortage.

City officials said they had reached an agreement with a major supplier Thursday night that would ensure emergency operations — fire, police, sanitation and work by the parks department to clean up downed trees — would continue uninterrupted.

Though Thursday marked a return to routine for many who ride the subway to work or celebrated the resumption of power, the scenes of long lines, fistfights at gas stations and siphoning at parking lots highlighted the difficult, uneven slog to recovery.

The losses from the storm will approach $50 billion, according to an early estimate from economists at Moody’s Analytics — about $30 billion in property damage, the rest in lost economic activity like meals and canceled flights. At the same time the death toll in New York City rose to 38, as rescuers continued to discover bodies while combing through coastal wreckage. Among them were the bodies of two boys, 2 and 4, who had been torn from their mother by raging floodwaters on Staten Island on Monday night.

The lack of power continued to bedevil efforts to address the damage. About 43 percent of customers in New Jersey and about 16 percent in New York State remained without electricity, and officials said that they expected power to be restored to all of Manhattan by Saturday. Those issues were only aggravated by the increasingly short supply of gas, particularly given that many suburban residents in New Jersey and elsewhere were heading to the stations to fuel generators, which provided the lone source of power and heat to homes across the region.

According to figures from AAA, of the gas stations it monitors, roughly 60 percent of stations in New Jersey and 70 percent on Long Island were closed.

At stations that were open, nerves frayed. Fights broke out Thursday at the block-long Hess station on 10th Avenue in Midtown Manhattan, forcing the Police Department to send three officers to keep the peace, a police official said. By evening, the police had to close two lanes of the broad thoroughfare to accommodate a line of customers stretching eight blocks, to 37th Street.

The ports and refineries that supply much of the region’s gas had been shut down in advance of the storm and were damaged by it. That disrupted deliveries to gas stations that had power to pump the fuel. But the bigger problem was that many stations and storage facilities remained without power.

Politicians were scrambling Thursday to increase the supply of fuel — the Port of New York and New Jersey opened just enough to allow boats carrying gas to move, and Gov. Chris Christie of New Jersey waived restrictions that make it harder for stations to buy gas from out-of-state suppliers. Mr. Christie’s office had warned that price gougers would be prosecuted, but drivers were reporting that some stations were charging more than $4 a gallon, even though the state had set gas prices at $3.59 on the highways last week.

Mr. Christie said Thursday afternoon that President Obama had sent 250,000 gallons of gas and 500,000 gallons of diesel fuel to the state through the Department of Defense, and he pledged to send more if needed.

Despite these steps the situation was not expected to get significantly better on Friday. Utility companies said power might not be fully restored until late next week.

In Paterson, N.J., the state’s third-largest city, the Police Department was trying to negotiate emergency contracts for gas, and short of that, said it would beginning siphoning it from other city vehicles to keep police cruisers running.

The Essex County executive, Joseph N. DiVincenzo Jr., said that the fuel shortage had become his No. 1 concern, causing officials to start limiting gas half a tank at a time to police and fire vehicles. “All 22 of our municipalities are having problems getting fuel,” he said. “Everyone’s on edge.”

Some drove hours out of their way, across state lines, in search of gas. Others tried their luck at a dozen stations, finding many roped off, or turned to Twitter, trading tips about where lines were long.

That is how Jason Brown, 25, of St. Albans, Queens, learned there might be gas at a BP station two miles away in Valley Stream, Nassau County. He walked there lugging a five-gallon Igloo cooler hoping to fill it with gas for his car — only to find a line stretching a quarter-mile along Sunrise Highway. When the generator pumping the gas failed, the crowd erupted into fights and police were called in to close the station.

“I’m trying to get gas for my family,” Mr. Brown said. “Everywhere you go, it’s either a riot or there’s no gas.”

The lines themselves only exacerbated the problem; reports in the local media provoked drivers to buy gasoline before stations ran out. Some spent what fuel they had searching for more and could be seen pushing vehicles toward relief.

“I just want to have it, because you don’t know how long this is going to last,” said Richard Bianchi, waiting in the half-mile line at the Sunoco in Union with a tank that was three-quarters full.

“People are panicking,” said Jimmy Qawasmi, the owner of a Mobil in the Westchester County town of Mamaroneck. “People must have heard something.”

Bloomfield Avenue, a traffic artery connecting several towns in Essex County, N.J., was unusually congested as drivers stopped to lean out their windows at every station: “You got gas?” Mr. Soni’s station in Montclair had received a delivery of 8,000 gallons at 4 p.m. Wednesday, but that had run out by 2:30 a.m. Thursday. A tanker truck passed by, prompting a cheer. “I’m empty!” the driver called out.

Up the road, a tanker turned into one gas station just down from where a crowd was waiting at another. The people waiting dashed across the street, only to see the tanker turn and go to the station where they had been waiting. The police were refusing to let the station open for three hours, but people were determined to hold out.

As Benito Domena, holding two gas cans, said: “The wait is just going to be worse elsewhere.”