British Airways (BA) and Unite, the cabin crew union, restarted talks on 2 August in a bid to solve the long-running dispute over pay and prevent further walkouts.
The first meeting, held under the supervision of mediator Advisory, Conciliation and Arbitration Service has been adjourned without agreement.
BA and Unite have decided to meet again next week for further talks, according to Reuters.
The ongoing dispute has resulted in a series of strikes, which have cost BA £150m ($238m).
In July, cabin crews voted against a revised pay offer by BA, but Unite members are yet to be balloted over a possible further round of strikes.
Unite also said it would take legal action against the airline over the removal of travel concessions from striking workers.