"If we don't find a solution to the conflict, there will be strikes from January 7," the source said, following a meeting with various Iberia union representatives.
Unions on Monday called off stoppages planned for December 14 and December 17-21 to avoid disrupting holiday travel.
The strikes would likely have hit Spain's image and Iberia's bottom line. Rival airlines would have suffered because of the absence of Iberia's baggage handlers.
The Spanish flag carrier and British Airways make up International Airlines Group IAG.L which said in November it would dismiss 4,500 workers at loss-making Iberia and cut salaries by between 30 and 50 percent for remaining employees.
Iberia said last week it would stop flying to destinations including Athens, Cairo and Havana in 2013, something the Spanish authorities said they did not agree on.
The company said it would hold new talks with the unions on Thursday. (Reporting by Robert Hetz, Writing by Clare Kane; Editing by Julien Toyer and David Cowell)
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