Southwest CEO Gary Kelly apologized to the tens of thousands of passengers who were stranded at U.S. airports over the weekend due to widespread flight cancellations.

"I want to apologize to all of our customers, this is not what we want," Kelly said in an interview on "Good Morning America" Tuesday. "Unfortunately, it just takes a couple of days to get things back on track."

One of those passengers, Fabricia Amara, couldn't take her 14-year-old daughter to see her neurosurgeon in Miami because of the operational meltdown.

"They did not handle it properly," Amara told ABC affiliate KTRK. "They have no answers for you, they tell you that there's nothing we can do."

Amara's flight was just one of more than 2,200 flights Southwest has canceled since Saturday.

The airline initially blamed the multi-day mess on air traffic control issues, bad weather and "other external constraints."

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But the Federal Aviation Administration (FAA) said in a statement that "there had been no air traffic control shortages since Friday," adding, "Some airlines continue to experience scheduling challenges due to aircraft and crews being out of place."

Kelly acknowledged air traffic control issues were not the cause, saying "a series of FAA Florida delay programs" on Friday contributed to the cancelled flights.

"There were no ATC issues over the weekend. That's absolutely true," Kelly said. "But I think any industry expert knows that it takes several days, if you have that large of an impact on the operation, to get the airplanes where they need to be and then to match the crews up with that."

The head of Southwest's pilot union blamed bad staffing for the disruptions.

"Until the company makes some changes in how they're doing business internally and scheduling our pilots, we're going to continue to see the problem," Capt. Casey Murray told ABC News.

Kelly said operations are "back to normal." According to FlightAware, there were 87 canceled Southwest flights as of 8 a.m. ET Tuesday.

"Things are much smoother today," he said. "We have a few more cancellations than we would normally have, but things are pretty well back to normal."

ABC News' Sam Sweeney contributed to this report.