American asked the Federal Aviation Administration to halt its flights until 5 p.m. EDT. Flights on regional affiliate American Eagle heading to Dallas, Chicago or New York's LaGuardia Airport have been stopped until 3:30 p.m. EDT.
Some passengers are stuck on planes while others can't make reservations.
Passengers are using social media to flood the airline with complaints.
American Airlines spokesman Kent Powell said Tuesday that the airline is trying to resolve the issues as quickly as it can.
On Twitter, American is sending out apologies but not offering customers much information about when the problem will be fixed.