Siptu representatives at Aer Lingus and the company's chief executive are to meet again on Monday morning to discuss the airline's intentions to shed 1,325 jobs.
Both sides met this morning for two-and-a-half hours and decided to reconvene on Monday to allow both sides a "period of reflection" on their position, according to a Siptu spokesperson.
Siptu is looking to secure a lifting of the September 14th deadline for receipt of redundancy applications.
Mr Willie Walsh said in a letter yesterday he was prepared to meet union negotiators this morning.
Siptu accepted the invitation and immediately called off general meetings it had arranged for tomorrow at Dublin, Cork and Shannon airports, which would have caused flights to be delayed.
The union is also seeking a process to be put in place for talks on the airline's restructuring plan, which includes cutting the 1,325 jobs, about a third of the total, across most areas of the company.