The FAA said in a statement the airlines were experiencing issues "with a flight planning weight and balance program called Aerodata".
Delays initially began popping up in New York, Boston, Chicago, and Miami. "We apologize to our customers for the inconvenience", American Airlines told Newsweek.
Southwest was also working to resolve a "system issue" which resulted in canceled flights for some customers, according to various company Tweets.
By midday, 3,400 US flights had been delayed, according to tracking service FlightAware, but it was unclear how many were related to the technical issue.
Southwest Airlines lifted an internal ground stop Monday morning after about 40 minutes.
Molinaro said the software issues were affecting Southwest, United, JetBlue, Delta and Alaska Airlines flights.
FlightAware, an airline tracking website, said Southwest had delayed 775 flights, or 18 percent of its US flights on Monday. SkyWest, a commuter airline affiliated with United and Delta Airlines, had over 200 flights delayed.
American Airlines said the technical issue was related to AeroData, a company that makes aircraft location and balancing technology. Check flight statues at the Birmingham airport here. The airline said after the systems resumed that the flight would arrive at 8.05 a.m. The airline did not anticipate flight cancellations. "Mainline operations and regional operations are impacted to varying degrees".