(CNN) -- Authorities imposed gasoline rationing on motorists in New York City and Long Island on Thursday, a day after a nor'easter added to the woes of a region still grappling with the damage left behind by last week's Superstorm Sandy.
The orders from Mayor Michael Bloomberg and Gov. Andrew Cuomo restrict private owners to buying fuel for their vehicles on either odd- or even-numbered days, depending on their license numbers. Commercial vehicles are exempt from the order, which they said is aimed at easing a fuel crunch caused when Sandy smacked the region.
"Drivers are still facing long lines, frustrations are only growing and it now appears that there will be shortages for possibly another couple of weeks," Bloomberg told reporters Thursday afternoon. "The best way, we think, to cut down the lines and help customers buy gas faster, to help gas stations stay open longer and to reduce the potential for disorder, is to alternate the days that drivers can purchase gas."
The order takes effect Friday morning. New Jersey, where Sandy made landfall October 29, put similar rules into effect last week in 12 counties.
At least 658,000 utility customers remained without electricity across the region, most of them in New York and New Jersey, with the nor'easter that swept through Wednesday only adding to those totals.
"The main thing is we need heat and electricity," Christine Holland, a relief coordinator in Brooklyn's Gerritsen Beach neighborhood, told CNN. Holland appealed to plumbers, electricians and boiler mechanics to volunteer their help to residents, as well as counselors for people still dealing with the trauma of last week's storm.
New Jersey Gov. Chris Christie told reporters Thursday morning that the nor'easter was responsible for 167,000 new outages, but praised utility workers who were trying to get the lights and heat back on.
"These men and women on the utility companies are working 16-hour days, every day," Christie said. "So I know that unless your power is turned on, that doesn't mean anything to you -- but I'm telling you, I've watched these people work. They were working last night through the snow."
Thursday's temperatures were in the mid-40s in much of the New York, New Jersey and Connecticut communities that were ravaged by Sandy, which killed 111 people in the region, knocked out power to millions and flooded large swaths of the heavily urbanized area. The new storm brought snowfalls ranging from two inches on Atlantic City, where Sandy hit, to more than a foot of snow in parts of Connecticut.
"Just what New Jersey needs now," said Justin Page of Montclair, about 10 miles west of Manhattan. "We have lost power where we never had before, and the winds are picking up dramatically, which is disturbing the debris left from Sandy."
About 6 inches of snow fell by Thursday morning on Newark, where Mayor Cory Booker called it "Mother Nature's one-two punch."
"It's testing the resolve and the grit of my state and my city and, obviously, this region," Booker said on CNN's "Piers Morgan Tonight."
The new storm crashed into the area barely a week after Sandy, which Cuomo said Thursday had inflicted $33 billion in damage to New York state and $50 billion to the region.
Freeport, along Long Island's southern coast, was one of the communities hit hard by the nor'easter. "This storm just made everything worse," Shanel Francis told CNN affiliate News 12. Sandy swamped her home with 4 feet of storm surge last week.
Bloomberg had urged residents in the city's low-lying areas -- especially Breezy Point, Hamilton Beach and Gerritsen Beach -- to "consider going someplace else" Wednesday night, "to be a little bit on the safe side."
But he issued no mandatory evacuation orders, other than for a handful of chronic-care facilities and an adult-care center in areas that were hit hard by Sandy.
"If people think you're crying wolf, the next time, when it's really a serious threat, they might not do it," the mayor said.
That was not the case in New Jersey, where the Brick Township Office of Emergency Management issued a mandatory evacuation order for all residents of low-lying waterfront areas of town.
Flights continued to be affected, and authorities advised air travelers to check with their carriers ahead of the storm.
"Airlines serving the Port Authority's major airports -- Newark Liberty International, John F. Kennedy International and LaGuardia -- have canceled all or a significant number of their flights" through Thursday morning.
CNN's David Ariosto, Tom Watkins, Tina Burnside, Marina Carver, Kristen Hamill, Katia Hetter, Julia Talanova and Rob Frehse contributed to this report.