A sprawling winter storm that battered southern, central and eastern U.S. states with heavy snow and frigid temperatures over the weekend has left multiple people dead and continued to snarl air travel and power grids.

The storm continued to disrupt thousands of flights Monday, and about 560,000 customers from West Texas to Maine were without power for a third day.

Forecasters told people to continue to expect similar subzero conditions Monday, with around 200 million Americans under weather alerts from the National Weather Service, covering ice storms, extreme temperatures and cold weather advisories.

New England could expect snow Monday night as the storm tapers off, and much of the country could face lingering cold on Tuesday, according to the weather service.

“The next several days we’re expecting further frigid conditions pretty much across the eastern two thirds of the U.S. with numerous record lows,” said Frank Pereira, a meteorologist with the weather-service prediction center. Parts of the country could see temperatures drop as low as minus 50 degrees Fahrenheit, Pereira said.

“We will see some additional snowfall across portions of the Northeast but overall we are not expecting additional, widespread, heavy amounts,” he added.

New York City Mayor Zohran Mamdani said that seven people were found dead outdoors over the weekend, adding that it was too early to determine the causes of death.

In Emporia, Kan., roughly 100 miles southwest of Kansas City, Kan., a 28-year-old elementary school teacher was found dead Sunday, just half a mile from where she had left a bar days before, according to local police. Rebecca Rauber was found by rescue teams Sunday covered in snow, the police said. It is thought she died of hypothermia shortly after leaving a local bar on Friday night.

Storm-related deaths also were reported in Louisiana, Michigan, the Dallas-Fort Worth metro area and Austin, Texas. The Tennessee Department of Health said late Sunday it had confirmed at least three weather-related fatalities.

Thousands of flights at East Coast hubs were canceled Monday, including a majority of departures from Boston Logan, John F. Kennedy International, LaGuardia, Newark Liberty International and Reagan National airports.

Around 21,000 flights in or out of U.S. airports have been canceled because of the storm, according to flight-data provider FlightAware, although restrictions on flights were improving Monday.

Around 5,500 flights in or out of U.S. airports were canceled Monday, according to FlightAware. Another 7,200 had been delayed. That is down from more than 11,600 flights canceled Sunday as the storm battered the Southeast and moved north.

Major air carriers said they would resume operations early this week as conditions improved. American Airlines removed a quarter of its flights that had been scheduled for Monday, while Delta Air Lines , Southwest Airlines and United Airlines all scrapped about 10% of their schedules.

New York and New England still faced travel restrictions. About 60% of flights out of Logan International Airport in Boston were canceled as of Monday afternoon, while roughly half of flights leaving New York City’s three area airports were canceled.

A business jet crashed on takeoff Sunday evening from Bangor International Airport in Maine, killing seven of the eight people on board, officials said. The Bombardier Challenger 600 crashed under unknown circumstances and “came to rest inverted and caught on fire,” the Federal Aviation Administration said. Bangor was under a winter storm warning at the time of the crash.

The storm knocked out power for about 560,000 homes and businesses as of Monday evening, according to PowerOutage.us, which monitors electrical outages. The south was hit the hardest. Tennessee reported 186,000 outages while Mississippi had about 144,000 and Louisiana had 104,000.

“It will be a prolonged restoration period,” said Keith Hayward , chief executive of Mississippi-based North East Power. In Tennessee, Nashville Electric Service said Monday that about 175,000 of its customers remained without power. Outages from the storm peaked at 230,000, marking the largest number of outages at one time with Nashville Electric Service, the utility said.

While the most severe precipitation had passed early Monday, the volume of snowfall a day earlier left treacherous conditions, complicating travel in major cities.

Parts of Boston saw nearly 17 inches of snow Sunday, while Newark recorded more than 12 inches, according to the weather service. In New York, parts of Manhattan saw nearly 15 inches of snow.

Canada felt some of the worst impacts of the storm, breaking several snowfall records. Toronto Pearson Airport saw more than 18 inches of snow Sunday, according to Environment Canada. Total snowfall at the airport so far this month has hit 34.7 inches, the most since records began in 1937.

Write to Gareth Vipers at gareth.vipers@wsj.com , Joseph De Avila at joseph.deavila@wsj.com and Alyssa Lukpat at alyssa.lukpat@wsj.com