Mayor Michael Bloomberg says that fully resolving the shortages at gas stations could take a few days.
Bloomberg spoke at a briefing Saturday.
Long lines of vehicles and pedestrians formed after Gov. Andrew Cuomo announced that the U.S. Department of Defense was opening the mobile fuel stations in New York City and on suburban Long Island.
The government then asked the public to stay away from the locations until emergency responders get their gas.
National Guard Col. Richard Goldenberg said Saturday afternoon that people who were already at the distribution sites would not be turned away.
More New Yorkers got power Saturday for the first time since Superstorm Sandy struck the region, but frustrations mounted over gasoline shortages as refueling sites turned into traffic jams of horn-honking confusion.
Gas rationing went into effect in northern New Jersey, while crowds lined up at free fuel distribution sites in New York's boroughs, where a limit of 10 gallons per person was imposed. New York officials then said emergency vehicles had the priority over the public.
"It's chaos, pandemonium out here," said Chris Damon, whose family was displaced from his home in the Queens neighborhood of Far Rockaway and are staying with relatives in Brooklyn. He circled the block for 3½ hours at the Brooklyn Armory, where the National Guard was directing traffic.
"It's ridiculous. No one knows what's going on," he said.
New York Gov. Andrew Cuomo had announced that the 5,000-gallon trucks from the Defense Department would set up the emergency mobile gas stations at five locations around the New York City metropolitan area.
"Do not panic. I know there is anxiety about fuel," he said.
After the long lines formed, New York state officials said the public should stay away from the refueling stations until emergency responders first got their gas and more supplies are then made available.
The scene was more orderly in hard-hit Staten Island, where a line of cars stretched for two miles under the supervision of police and National Guard troops. Another 400 people were on foot, carrying gas cans.
As gas rationing went into effect at noon in northern New Jersey, police began enforcing rules to allow only motorists with odd-numbered license plates to refuel. Those with even-numbered plates must wait until Sunday.
Jessica Tisdale of Totowa waited in her Mercedes SUV for 40 minutes at a gas station in Jersey City, but didn't quite understand the rules and was ordered to pull away because of her even-numbered plate.
"Is it the number or the letter?" she asked around 12:10 p.m. "I don't think it's fair. I've been in the line since before noon. I don't think it's fair. There's no clarity."
The officer who waved her out of line threw up his hands and shrugged.
At an Exxon station in Wall, N.J., Kathryn Davidson was unaware of the start of rationing but beat the noon deadline despite a 45-minute wait in line and an even-numbered plate.
"How are people supposed to know?" said Davidson, 53, who said it reminded her of the 1970s, when a similar plan was in place.
"There were fistfights and everything. It got nasty," she said. "Everyone seems pretty pleasant as of right now."
In Washington, President Barack Obama visited the headquarters of the Federal Emergency Management Agency for an update on superstorm recovery efforts and said "there's nothing more important than us getting this right."
"Obviously we've now seen that after the initial search and rescue, the recovery process is difficult and it's painful," Obama said. "But I'm confident that we will continue to make progress as long as state and local and federal officials stay focused."
Obama cited the need to restore power; pump out water, particularly from electric substations; ensure that basic needs are addressed; remove debris; and get federal resources in place to help transportation systems come back on line.
About 2.6 million people remained without power in six states after Sandy came ashore Monday night.
About 900,000 people still didn't have electricity in the New York metropolitan area, including about 550,000 on Long Island, Cuomo said.
About 80 percent of New York City's subway service has been restored, he added.
The storm forced cancellation of Sunday's New York City Marathon. Mayor Michael Bloomberg reversed himself Friday and yielded to mounting criticism about running the race, which starts on hard-hit Staten Island and wends through all five of the city's boroughs.
Bloomberg, who as late as Friday afternoon insisted the world's largest marathon should go on as scheduled, changed course shortly afterward amid intensifying opposition from the city comptroller, the Manhattan borough president and sanitation workers unhappy they had volunteered to help storm victims but were assigned to the race instead. The mayor said he would not want "a cloud to hang over the race or its participants."
Bloomberg, in his first comments since canceling the marathon, said he fought to keep it going but the controversy was becoming "so divisive" and too much of a distraction.
"I still think that we had the resources to do both, and that we want people to be able to take a break and that sort of thing. ... It's a big part of our economy," Bloomberg told WCBS-TV on Saturday during a visit to the borough of Queens. As he spoke, he was met by catcalls from residents angry about the city's response to the storm.
Many runners understood the decision to call off the marathon. The overall death toll from the superstorm was 105, including 41 in New York City. The widespread power outages made many New Yorkers recoil at the idea of police protecting a foot race and evicting storm victims from hotels to make way for runners.
The cancellation forced runners to deal with what to do with no race.
More than half of the 40,000 athletes were from out of town. Their entry fees were paid. Their airline tickets were purchased. Their friends and family had hotel rooms. And all week the race was a go, even after Sandy came ashore Monday.
"I understand why it cannot be held under the current circumstances," Meb Keflezighi, the 2009 men's champion and 2004 Olympic silver medalist, said in a statement. "Any inconveniences the cancellation causes me or the thousands of runners who trained and traveled for this race pales in comparison to the challenges faced by people in NYC and its vicinity."
ING, the financial company that is the title sponsor of the marathon, said it supported the decision to cancel. The firm's charitable giving arm has made a $500,000 contribution to help with relief and recovery efforts and is matching employee donations. Sponsor Poland Spring said it would donate the bottled water earmarked for the marathon to relief agencies, more than 200,000 bottles.
"When you have a significant amount of people voicing real pain and unhappiness over its running, you have to hear that. You have to take that into consideration," said Howard Wolfson, deputy mayor for government affairs and communications.
"Something that is such a celebration of the best of New York can't become divisive," he said. "That is not good for the city now as we try to complete our recovery effort, and it is not good for the marathon in the long run."
Each day has brought signs of recovery.
Aida Padilla, 75, was thrilled that the power at her large housing authority complex in New York City's Chelsea section had returned late Friday.
"Thank God," said Padilla, 75. "I screamed and I put the lights on. Everybody was screaming. It was better than New Year's."
Asked about whether she had heat, she replied, "hot and cold water and heat! Thank God, Jesus!"
But on Staten Island, there was grumbling that the borough was a lower priority to get its services restored.
"You know it's true," said Tony Carmelengo, who lives in the St. George section of Staten Island and still does not have electricity.
Added his neighbor, Anthony Como: "It's economics. Manhattan gets everything, let's face it."
The governor said the New York area had a strong sense of community, "but until you have your lights on you're not happy."
"We're not going to stop until we have every house and every home restored. ... This was truly a crisis, but it requires patience," Cuomo said.
NYU Langone Medical Center, one of two New York hospitals that had to evacuate patients at the height of the storm, said it would reopen Monday, although some doctors would see patients at alternate sites.
Seven backup generators at the hospital failed Monday night, forcing the evacuation of 300 patients.
At Bellevue Hospital Center, some 700 patients had to be evacuated after the power failed. An official there said the hospital could be out of commission at least two more weeks.
New Jersey Gov. Chris Christie said he would make public a list of when New Jersey utility companies intend to restore power to each community. Even if they end up working faster or slower, he said, residents will have a sense of when power will be restored so they can plan their lives a bit better.
Commuter rail operator NJ Transit said it would have more service restored in time for the workweek to start Monday, most of Atlantic City's casinos reopened, and many school districts decided to hold classes on Thursday and Friday — days previously reserved for the New Jersey Education Association's annual conference, which has been canceled.