Lufthansa was forced to ground flights at Frankfurt on February 15 after what it said was an external telecommunications line failure.
The failure "had a major impact" on Lufthansa's IT system, which was later in the day "up and running again", according to the carrier.
Inbound and outbound flights were said to be resuming, with Lufthansa stating it "expects the operational situation to improve".
However Lufthansa's social media feeds showed passengers continuing to ask about flight schedules late into the afternoon, with the carrier replying in some cases that passengers should check with airports, including at hubs from where flights to Frankfurt were to depart.
The outage came two days ahead of strikes affecting seven German airports, with Munich on February 15 requesting permission to cancel commercial flights as it expected to be "massively affected" by the industrial action.