The pilots had initially planned what would have been a very expensive four-day strike from April 13-16 for Lufthansa, Lufthansa Cargo, and subsidiary Germanwings.
But now the two sides late on Wednesday agreed to take their dispute to mediation, they said.
The dispute between Cockpit and Lufthansa has been brewing for months. The union, which represents some 4,500 pilots, has been trying to pressure the airline into providing better wage contracts.
In late February Cockpit called a first round of strikes for Lufthansa pilots, but after just one day a Frankfurt court stopped the industrial action.
The company had asked authorities to prevent the four-day strike from continuing, calling it “disproportionate.” The strike cost Lufthansa €48 million, and the first day alone grounded almost half of the airline's flights.
Like most airlines, the German flag carrier is still feeling the pinch of the global economic crisis, but Cockpit has said its members deserve a 6.4-percent pay raise and job guarantees.
Lufthansa, Europe's biggest in terms of passenger numbers, reported last month a 2009 net loss of €112 million owing to a slump across the sector, and said revenues should post "a slight recovery" this year.