American Airlines flights out of Phoenix Sky Harbor International Airport now have resumed.
The Dallas-based carrier grounded flights across the country earlier Tuesday because of an outage of its main reservations system.
Flights into American's five biggest cities -- New York, Dallas, Los Angeles, Chicago and Miami -- were stopped until the problem was fixed.
Sky Harbor officials five departing and four arriving American Airlines flights to and from Dallas and Chicago were cancelled.
American says its reservations system now has been fully restored, but flight delays and cancellations still are possible.
Officials with the carrier are urging travelers to check their flight status with the airline before coming to the airport.