Power outages and distribution issues after Hurricane Sandy have created long lines of customers at gas pumps, The Wall Street Journal reported.
"There will be more of a supply of gasoline and more of a distribution," Cuomo said at a news conference. "That does not mean there will be a total alleviation of the problem in the immediate future, but it is getting better."
Cuomo said there are continuing issues with delivery and distribution.
"We're not 100 percent sure when the system will [fully be] up and running," he said.
Meanwhile, with 2.4 million people in the United States without heat after Hurricane Sandy, temperatures dipped into the 30s and may not top 50 Sunday, forecasters said.
The National Weather Service said temperatures were in the 30s in Belle Harbor, N.Y., New York City and Cape May, N.J. Saturday night into Sunday morning. The service said it doesn't expect temperatures in those areas to top 50 degrees Sunday, and without power to supply heat to many residents, patience is running low, CNN reported Saturday.
"We covered two children with a blanket freezing and shivering here trying to get food last night," said Rockaway resident Lauren O'Connor, who came out to help those suffering form the cold. "We said we had to do something."
New York City Mayor Michael Bloomberg encouraged those without power to either go to a shelter or find another "warm place" to stay.
"Please, I know sometimes people are reticent to take advantage of services -- the cold really is something that is dangerous," he said.
Meanwhile, Bloomberg and Cuomo said they expect the Metropolitan Transportation Authority to restore up to 90 percent of subway services by Sunday, up from 80 percent Saturday.
Stretches of cars are still lining up at gas stations throughout the region, with about 70 percent of gas stations from Interstate 95 and north not operating Saturday, New Jersey Gov. Chris Christie said.
Those that aren't operating have gas, but not to power to run the pumps, he added. About 95 percent of gas stations south of Interstate 95 were working.
Drivers in New York City and Long Island were able to fill up Saturday directly from 5,000-gallon fuel tankers moving throughout the area, CNN reported.
On a positive note, the Port of New York and New Jersey is open to all vessels with a small exception, the Coast Guard said. Water has been removed from the World Trade Center work site, Cuomo said, and about $28 million in federal disaster emergency grants have been earmarked for nine counties in New York.
The U.S. death toll from Hurricane Sandy rose Saturday, reaching 113, the Los Angeles Times reported.
Notable deaths of 2014 [PHOTOS]