(CNN) — [Breaking news update, published at 10:49 a.m. ET]

The winter storm death toll has risen to 34 in Erie County, New York, as crews continue to clear roads and first responders check on people they couldn't reach days ago as the catastrophic weather system swept the nation, officials there said Wednesday.

Twenty-six of those who died were found in Buffalo, while seven were located in the suburbs, Erie County Executive Mark Poloncarz said in a news conference, adding he did not know where one person was found.

[Original story, published at 10:11 a.m. ET]

Emergency services have been restored in Buffalo, New York, officials said, as crews continue to clear roads and first responders check on people they couldn't reach days ago when a deadly winter storm swept the nation.

At least 31 people have died in New York's Erie County, where Buffalo was buried with nearly 52 inches of snow, trapping residents at home — many without heat as the Christmas weekend blizzard took out power lines. At least 25 others across 11 US states also have been reported dead in the storm.

A driving ban remains in effect Wednesday in Buffalo amid a two-day effort to clear at least one lane on every street to accommodate emergency responders, according to the city and Erie County Executive Mark Poloncarz. They're still hampered, though, by hundreds of vehicles abandoned in the snow, hazardous driving conditions and snow-covered lanes, with emergency and recovery vehicles still getting stuck, Poloncarz spokesperson Peter Anderson said Tuesday.

The county is bringing in 100 military police, plus New York State Police, to manage traffic control "because it has become so evident that too many people are ignoring the [driving] ban," Poloncarz said. Officials also are working to coordinate deliveries of fuel to emergency crews and grocery supplies to markets, he said.

"It's the reason why you need to stay off the road in these impacted areas, because we need to be able to get those resources to where they need to be so that the shelves are in fact stocked and ready to go," Poloncarz said.

Meantime, Buffalo is bracing for possible flooding as rising temperatures being to melt the massive amount of snow and 2 inches of rain is forecast through the weekend. The flood risk is small, the National Weather Service said.

For now, authorities are focusing on welfare checks and getting people to hospitals after hundreds of calls for help went unanswered as the storm slammed the area, Erie County Sheriff John Garcia has said.

Amid the frigid, whiteout conditions, "people ... got stranded in their vehicles and passed away in their cars. We have people that were walking during blizzard conditions and passed away on the street, passed away in snowbanks," Buffalo Mayor Byron Brown said. "And we have people that were found that passed away in their homes."

At least one reported death in Erie County has been attributed to an EMS delay, Poloncarz told CNN on Tuesday. "Our emergency responders could not get to the person because of the snow," he said. "They were blocked, and by the time they got there it was too late."

This storm marked the first time the Buffalo Fire Department could not respond to emergency calls because of severe conditions, Poloncarz said, citing the agency's historian. Two-thirds of the equipment dispatched to help clear winter snow during the height of the storm also got stuck, he said.

The blizzard — which Gov. Kathy Hochul called a "once-in-a-generation storm" — has drawn many comparisons to Buffalo's infamous blizzard of 1977 — a powerful storm that left 23 people dead.

"The blizzard of '77 is considered the worst storm in Buffalo history," Poloncarz said Monday. "Well, unfortunately, this has already surpassed it for deaths."

Nationwide death toll rises

Anndel Taylor, 22, was found dead in Buffalo over the holiday weekend after getting trapped in her car by the blizzard, her family said.

After losing contact with her, the family posted her location to a private Facebook page related to the storm to ask for help, and a man called to say he had found her without a pulse, her sister said.

The winter storm's grim effects have been widespread, with at least 56 storm-related deaths reported across several states:

• New York: In addition to the 31 deaths in Erie County, one fatal carbon monoxide poisoning was reported in Niagara County.

• Colorado: Police in Colorado Springs reported two deaths related to the cold since Thursday, with one man found near a building's power transformer, possibly seeking warmth, and another in a camp in an alleyway.

• Kansas: Three people died in weather-related traffic accidents, the Highway Patrol said Friday.

• Kentucky: Three people died, officials have said, including one involved in a vehicle crash in Montgomery County.

• Missouri: One person died after a van slid off an icy road and into a frozen creek, Kansas City police said.

• New Hampshire: A hiker was found dead in Franconia on Christmas morning, said Lt. James Kneeland, a spokesperson for the New Hampshire Fish and Game Department.

• Ohio: Nine people died as a result of weather-related auto crashes, including four in a Saturday morning crash on Interstate 75 when a tractor-trailer crossed the median and collided with an SUV and a pickup, authorities said.

• South Carolina: Two men — including a 91-year-old who went outside on Christmas Day to fix a broken water pipe — died due to the storm in Anderson County, the coroner's office there said. The other victim died on Christmas Eve after his home lost power.

• Tennessee: The Department of Health on Friday confirmed one storm-related fatality.

• Vermont: One woman in Castleton died after a tree fell on her home, according to the police chief.

• Wisconsin: The State Patrol on Thursday reported one fatal crash due to winter weather.

8 arrested for alleged looting

With flooding possible in Buffalo, crews are focused on clearing key snowbanks, officials said. Still, "it should take around an inch of rain from this system before flooding becomes a concern," the weather service said.

City leaders are working with the National Weather Service "not only to reflect back on what happened this past week but also what potentially could come," Department of Homeland Security and Emergency Services' Daniel Neaverth said.

All major highways across Western New York, including New York State Thruway, had reopened by Tuesday — "a sign that we are finally turning the corner on this once-in-a-generation storm," Hochul said.

Buffalo got another 1.6 inches of snow on Tuesday, bringing the total since Friday to 51.9 inches and the December total to 64.7 inches, the weather service said. Overall, Buffalo has gotten 101.6 inches this winter season, CNN meteorologist Robert Shackelford said.

Conditions are improving and the lake-effect snowfall has finally stopped, he noted. Warm temperatures are forecast for at least the next week, with Buffalo due for highs in the upper 30s on Wednesday and the 40s through the weekend.

Officials also have responded to a few reports of looting. Eight people had been arrested in Buffalo through Tuesday evening in connection with suspected winter storm looting, according to a tweet from the Buffalo Police Department.

"It is horrible that while residents of our community have died in this storm that people are out looting," the mayor said, but noted, "This is a minority of individuals."

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