Lufthansa resumed flights on Saturday after cabin crew agreed to end strike action that stranded thousands of passengers.
The airline had cancelled approximately half of its scheduled 1800 flights because of the stoppage.
The UFO union representing cabin crews and Lufthansa will now go into formal mediation talks.
Lufthansa has also made concessions on the use of temporary workers.
The BBC reports UFO is seeking a 5% pay increase for cabin crew and assurances on jobs.
However, Lufthansa has not improved its offer of a 3.6% pay rise in return for longer hours.
The union represents about two-thirds of Lufthansa's 19,000 cabin crew.
Lufthansa is currently undergoing a 1.5 billion euro ($US1.9 billion) cost-cutting programme to offset rising fuel costs and tackle competition from low-cost and Gulf carriers.
The airline reported a 24% drop in second-quarter profits to 229m euros compared with a year earlier.