Southwest Airlines is promising people who have purchased tickets with them will actually be flying this weekend.

After canceling thousands of flights for several days in a row, at the peak of the holiday rush, Southwest Airlines has released a statement with a more positive outlook for New Year's Eve and New Year's Day.

"We plan to return to normal operations with minimal disruptions on Friday, Dec. 30," the company said Thursday.

"We are encouraged by the progress we've made to realign Crew, their schedules, and our fleet," the statement continued, before adding the company is "eager to return to a state of normalcy."

Company officials have been directing consumers who have been impacted by the cancellations to an online portal where people can submit refund and reimbursement requests for meals, hotel and alternate transportation. People can also visit the link to be reconnected with their baggage.