Southwest Airlines is facing a class-action lawsuit after a passenger said the carrier did not provide refunds to passengers who were stranded after an operational meltdown in late December caused it to cancel over 15,000 flights.

Eric Capdeville filed the lawsuit in the Eastern District of Louisiana on Dec. 30 over his Dec. 27 flight to Portland. He accused Southwest of a breach of contract of carriage mandates refunds for canceled fights.

Capdeville says he and other passengers were only offered a credit.

The contract states Southwest will give refunds for canceled fights, and reimburse customers for costs like hotels, meals, and a rental car.

"Southwest's failure to provide prompt refunds for canceled flights violates not only its own contract of carriage but also federal law," the lawsuit said.

The lawsuit added that Southwest did "not offer any comparable accommodations on another flight." The contract also states that it will at least offer such compensation.

Southwest's flight cancellation issues disrupted thousands of flights during the holidays. Refunds are expected to cost Southwest more than $5 million.

Southwest's reputation has taken a severe hit. The company could also additional lawsuits.

Southwest said in a statement on Tuesday that it is putting in "high priority efforts" to fix problems for its customers.

"There are several high-priority efforts underway to do right by our customers, including processing refunds from canceled flights, and reimbursing customers for expenses incurred as a result of the irregular operations," the company said.

On Tuesday, Southwest offered 25,000 Rapid Rewards points worth more than $300 to the members of its frequent-flier program as compensation.

"I know that no amount of apologies can undo your experience," Southwest Chief Executive Bob Jordan said in an email sent to members.