REUTERS/Carlo Allegri
The airlines was forced to cancel more than 400
"We are very sorry," Horton said in a video posted to the airline's Facebook page Tuesday evening.
Speaking from the airline's operation control center in Dallas-Fort Worth, Texas, he explained that a software issue had affected both primary and backup systems.
In a statement Tuesday, American Airlines said it would not charge for reservation changes, and would offer full refunds to customers who chose not to fly. It also allowed its customers to rebook with another airline, and said it would honor the difference in price.
"We don't like to let you down," Horton said in the video.
"Again, we're very sorry for that, and we'll continue to work hard to earn your loyalty."
United Airlines suffered a series of reservation system outages last year, as it merged its systems with Continental.
Here's Horton's apology: