Replying to questions in the National Assembly on Wednesday, Nosiviwe Mapisa-Nqakula said she considered it a follow-up to a previous question on oversight, and would not answer it.
The Democratic Alliance had referred to a trip General Solomon Shoke took to Malaysia with Emirates, and had asked what Mapisa-Nqakula was doing to keep costs down and to stay in line with a National Treasury directive forbidding first-class flights.
DA MP David Maynier submitted that Shoke's flight showed the department was its own enemy and wasted millions of rand, even though it was in trouble.
When Mapisa-Nqakula refused to answer, DA chief whip John Steenhuisen objected and said it was not up to her to decide whether she was going to answer a question or not.
Mapisa-Nqakula eventually said: "Yes there are cost saving measures."
The DA said on Monday it would ask the auditor general to investigate the flight issue.