No flights were allowed to take off from the continental US for more than four hours from 15:54 EST (19:54 GMT) on Friday.
More than 3,500 flights were cancelled and more than 2,000 delayed in the US on Saturday, according to tracking website Flight Aware, as knock-on disruption continues.
In some cases, passengers were left stuck inside planes on the tarmac, unable to take off or to return to the gates. Some international flights were allowed to depart US airports, in an apparent effort to clear space.
Duffy warned that a similar issue could arise again unless the US Congress approved upgrades to air traffic control infrastructure.
US President Donald Trump has requested $30.1bn for the upgrades. Both chambers of Congress are currently controlled by the Republican Party.
