Commercial general manager Theunis Potgieter and legal and risk head Sandra Coetzee resigned on Monday.
Tlali said SAA would shortly issue a statement on the matter.
Earlier, Gigaba's office said SAA would begin searching for a new chief executive after Mzimela quit on Monday.
"Government is committed to work with the SAA board and management to ensure that SAA is stable and becomes a financially stable airline," it said in a statement.
"The board will, without delay, commence a process of finding a new CEO of SAA to take the national airline forward."
It said board chairman Vuyisile Kona had accepted Mzimela's letter of resignation.
"... Ms Mzimela will be available to provide the SAA board with a proper hand-over report to ensure a smooth transition."
Gigaba's spokesman Mayihlome Tshwete said the resignation was "not with immediate effect" and that Mzimela would stay with the airline until a suitable interim CEO could be appointed.
The Business Day website BDLive reported on Monday that Mzimela had described her resignation to her staff as "not a random move".
"I have given this decision careful thought and feel that now is the best time to relinquish my position as your CEO and allow somebody else to pilot the company into the future," she was quoted as saying.
Mzimela's resignation comes weeks after SAA chairwoman Cheryl Carolus and six board members resigned.
SAA was expected to report a R1.25bn loss for the year ended March 31, when it holds its annual general meeting next week.
Last week, the airline won support from National Treasury after hard negotiations between it and the public enterprises department to support the airline, which according to the previous board has a debt to equity ratio of -359%, the website reported.
Last week, the Treasury agreed to a R5bn guarantee to enable SAA to borrow from financial markets.
Source: Sapa via I-Net Bridge
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