Across the US, at least 62 people have died in weather-related incidents.
In Buffalo, a state official said that military police are being brought in to help manage traffic in the city, where a driving ban remains in place.
Looting has been reported in parts of the city during the emergency.
The winter storm has also forced the cancellation of thousands of flights, including about 4,800 on Tuesday morning alone. Thousands of passengers have been left stranded at airports across the country.
Conditions are now expected to improve, with very little snowfall on Tuesday and slightly warmer weather on the way.
At a news conference on Tuesday, officials in New York’s Erie County – which includes Buffalo – said that the death toll is expected to rise as search and rescue operations continue. The 28 confirmed dead were all in Buffalo.
“All of the numbers have not caught up at this time,” Buffalo Mayor Byron Brown said. “We know that the [Erie] county number is larger.”
More than 4,000 people in the area remain without power after the storm, which Mr Brown said was “probably” the worst of most residents’ lifetimes. At the peak of the storm, about 20,000 people were without power.
Mr Brown added that there had been an “improvement” in the city, with very little snowfall and an absence of whiteout conditions allowing officials “significant progress” as they clear vehicles and restore power.
Officials warned that the warming temperatures in the region might lead to additional problems, including flooding as snow thaws.
In Erie County, city authorities on Tuesday were removing ice and blockages from storm drains ahead of what officials referred to as a “rapid melt”.
Mark Poloncarz, executive of Erie County where Buffalo is located, said that 100 military police officers and additional state police were being brought in to help control traffic in the area, where conditions remained “ugly” on many local roads.
Buffalo Police Commissioner Joseph Gragmalia said that looting is “still going on”. Four people have so far been arrested.
“This isn’t people stealing food and medicine and diapers,” he said. “They’re destroying stores. They’re stealing televisions, couches, whatever else they can get their hands on. They’re opportunists.”
On Monday, US President Joe Biden approved an emergency declaration allowing federal support for New York State. “My heart is with those who lost loved ones this holiday weekend,” he tweeted.
Neighbouring state New Jersey also sent emergency services to New York state to provide further assistance.
State Governor Kathy Hochul, a native of Buffalo, described the storm as “the blizzard of the century”.
“It is [like] going to a war zone, and the vehicles along the sides of the roads are shocking.”
Officials in New York have said that emergency personnel were forced to go from car to car searching for survivors of the storm, sometimes finding bodies in cars and snow banks.
Mr Poloncarz said that some of the fatalities died from cardiac arrest while ploughing snow, with Buffalo state issuing a “Shovel Smart” warning, notifying people that over-exertion from shovelling snow can cause heart attacks or back injuries. While three additional deaths were confirmed by Tuesday morning, two deaths that had been reported earlier were deemed a “non-storm related”, he added.
Harrowing tales
Some local residents recounted harrowing escapes from the storm over the last several days.
One local family with young children – aged two to six – had to wait for 11 hours before being rescued in the early hours of Christmas Day (Sunday).
“I was basically just hopeless,” the father, Zila Santiago, told CBS News. He said he managed to stay warm by keeping the engine running, and kept distress at bay by playing games with the children.
Ditjak Ilunga from Gaithersburg, Maryland, told CBS News he was on his way to visit relatives in Hamilton, Ontario, with his daughters when their SUV was trapped in Buffalo.
After spending hours with the engine running he made the desperate choice to risk the howling storm to reach a nearby shelter.
He carried six-year-old Destiny on his back while 16-year-old Cindy clutched their Pomeranian puppy, and followed his footprints in the snow drifts.
“If I stay in this car I’m going to die here with my kids,” Mr Ilunga recalled thinking.
He said he cried when the family walked through the shelter doors. “It’s something I will never forget in my life,” he said.
While the largest death toll has been reported in New York, storm-related deaths have been reported across the US, including Vermont, Ohio, Missouri, Wisconsin, Kansas, and Colorado.
Over the weekend, an estimated 250,000 homes and businesses experienced blackouts, although power has steadily been restored. Still, tens of thousands of people remained without power on Tuesday.
In Canada, the central province of Ontario and Quebec, in the north-east, bore the brunt of the storm.
Ontario’s Prince Edward County, along Lake Ontario, declared a state of emergency and had to take snow ploughs off the streets because they were in danger of getting stuck, Mayor Steve Ferguson told CBC News.
Four fatalities earlier occurred when a bus rolled over on an icy road near the town of Merritt, in the western province of British Columbia.
