Although the union, Sepla, did not issue a comment, the airline spokeswoman said the two sides had agreed to have a mediator facilitate their negotiations.
ThinkSpain said the agreement was announced Monday with representatives from the Employment and Social Security Ministries on hand.
Pilots had previously released a schedule of 24-hour strikes. They had planned on 24 of those job actions to take place between March 16 and May 28.
The union is seeking job protection.
A discount airline, Iberia Express, is scheduled to begin service March 25. Pilots fear the new low-cost airline will cost them thousands of jobs, ThinkSpain reported.