Flights across Europe could be severely disrupted this week after German air traffic controllers agreed to strike over pay.
The GdF union said its board had rejected the management's latest offer.
However, it added that it is still prepared to comply with a request from the federal government and meet once again for talks with an arbiter.
The union said that a strike could take place as early as Wednesday.
A strike must be announced with 24 hours notice, and the union did not immediately elaborate whether it was planning short walkouts in a few regions, or a full-scale strike across Germany.
The DFS air traffic services agency sent the dispute over pay and working conditions to arbitration in early August, but the union partly rejected the outcome a month later.
New negotiations based on the arbitration's result broke down late Friday. Both sides have accepted the arbiter's compromise of a general salary raise of 5.2%, but the union wants more people to be promoted faster.
The DFS has about 6,000 employees, co-ordinating about 10,000 flights a day, making Germany's skies Europe's busiest.