KwaZulu-Natal transport MEC Willies Mchunu on Monday dismissed calls for him to resign as premature and irrelevant.
"It is premature to call for anybody to be penalised for this incident before the investigation is concluded," he said in a statement.
"Only after the investigation can we then determine whether anybody can be blamed, that is what justice demands."
Mchunu was responding to calls by the Inkatha Freedom Party for him to resign following the deaths of seven people during a Road Traffic Inspectorate recruitment drive in Pietermaritzburg.
The seven died during a 4km run, which was part of a fitness test held at the city's Harry Gwala stadium on Thursday and Friday. One of the seven allegedly committed suicide.
Mchunu suspended all tests for Road Traffic Inspectorate jobs while his office investigated the matter.
"To us this is a tragedy and we don't think any blame game will assist. I have started a thorough investigation... which I will then submit to the premier for his consideration to take the process forward."
More than 34 000 people had qualified to apply for the 90 advertised trainee posts. A total of 15 600 applicants attended the fitness test on Thursday, and a similar number on Friday. An unknown number of them collapsed due to the heat. Many were taken to hospital.
The SA Communist Party in KwaZulu-Natal commended Mchunu for his swift action.
IFP MPL Blessed Gwala said: "What happened in Pietermaritzburg was a classic display of being power-drunk, to an extent treating ordinary suffering people as subhuman.
"No one in their right mind could in the first place short-list about 35 000 people for just 90 jobs."