Lufthansa chief Carsten Spohr said Wednesday the plane operated by its low-cost subsidiary Germanwings that crashed in the French Alps had been "in perfect condition".
"It is inexplicable," he said when asked if he had further information on the cause of the crash Tuesday that claimed the lives of 144 passengers and six crew.
"The plane was in perfect condition and the two pilots were experienced."
He said Lufthansa would begin offering flights from Duesseldorf and Barcelona to the southern French city of Marseille from Thursday to allow the relatives of victims -- most of them German and Spanish -- to reach the crash region.
"Our priority right now is to help the families," he told reporters.
The company's chief financial officer Simone Menne said Tuesday had been "without a doubt the toughest day (in the history) of Lufthansa".
"We don't ever, ever want to experience something like this again," she said.
The last fatal crash of a Lufthansa plane also involved an Airbus A320. It caught fire on landing near Warsaw in September 1993, killing two people and injuring 54.
Germanwings said none of its aircraft has ever been involved in a crash before Tuesday's disaster.