Weather-related flight cancellations and delays that snarled U.S. commercial air traffic over the holiday weekend dragged on through Monday, with Southwest Airlines accounting for the bulk of the lingering disruptions a day after Christmas.

More than 3,800 U.S. airline flights were cancelled on Monday, including 2,800 operated by Southwest, or nearly 70 per cent of the carrier's total scheduled for the day, according to the flight tracking service FlightAware.

Delays were reported for more than 7,100 U.S. flight departures and arrivals overall, with several hundred by Southwest.

"Challenges are impacting our customers and employees in a significant way that is unacceptable,” Southwest said in a statement, citing“consecutive days of extreme winter weather.”

The Dallas-based airline, one of the world's largest low-cost carriers, said it anticipated the disruptions would continue in the days heading into the New Year holiday travel period at the end of this week.

The U.S. Transportation Department said late on Monday it would examine the large number of Southwest Airlines cancelled and delayed flights in recent days to determine if they were in the airline's control, calling them“unacceptable.”

Commercial airline traffic has been upended since last week as an Arctic blast coupled with a massive winter storm dubbed Elliott took shape over the Midwest and swept over much of the United States in the lead-up to the Christmas holiday weekend.

The resulting surge in cancellations and delays, coupled with long lines and missing luggage at airports, spoiled wintertime vacation plans for countless U.S. airline customers during one of the busiest travel periods of the year.

Kyle Goeke, 29, said he would be stuck in Seattle for days after Alaska Airlines cancelled his flight, scheduled for early Monday, from Seattle to Missoula, Montana.

He had already travelled from Washington, D.C., to Seattle late on Sunday and said he hadn't slept at all overnight, forced instead to make lodging arrangements in Seattle.

"Luckily, I have a friend here in this city to help me out, many others are just left by themselves,” he told Reuters.

Many would-be passengers took to social media to express frustration and to try to get a response from airlines.

David Sharp said on Twitter his Southwest Airlines flight from Denver to St. Louis was cancelled and the next flight was not available for another two days. He said he would rent a car and drive to his destination.

Southwest Airlines said on Monday it was facing a large number of travel inquiries from customers and was doing its best to get its network back to normal.

Voice actress Grey DeLisle tweeted to Southwest Airlines: ”Flight 1824 from Nashville to Burbank was cancelled due to Elliot and we haven't received any rebooking! The kids' daddy has already missed Christmas now and his luggage is lost with medication in it! Customer Service line busy. Help!”

"My brother's Southwest Airlines flight out of Philly back to El Paso was cancelled today and the best they could do was out of Baltimore on Tuesday morning! Nothing anyone could do but so much travel insanity,” wrote another Twitter user named Alex Gervasi.

Some luggage was left unclaimed at William P. Hobby Airport in Houston for two days, while many passengers arrived unable to locate their bags, local media reported.

Madeline Howard said on Twitter she was told by Southwest that her luggage was flying to a different airport despite her flight having been cancelled.