Public enterprises minister Pravin Gordhan is set to meet unions representing striking SAA employees on Tuesday in an effort to resolve the stalemate over wages.
The industrial action has entered its fifth day.
The state-owned airline has cancelled hundreds of flights since the strike began on Friday, saying the stoppage is costing R50m per day and jeopardising talks with potential lenders.
Irvin Jim, general secretary for the National Union for Metalworkers of South Africa (Numsa), which called the strike alongside the South African Cabin Crew Association (Sacca), said the unions would meet Gordhan on Tuesday to discuss the strike.
Sacca deputy president Christopher Shabangu also confirmed the meeting, saying it was "trying to find a solution to ending the strike".
Gordhan's spokesperson could not be reached for comment.
The strike has cast doubt on the survival of the airline, which hasn’t turned a profit since 2011 and is reliant on state bailouts. SAA said on Monday its international flights were operating on schedule while some domestic passengers would face more cancellations on Tuesday and Wednesday.
The unions have threatened to shut down South Africa's entire aviation industry by extending industrial action beyond the state-run airline.
SAA is expected to give updates on the strike on Tuesday.