He said these were the findings of a commission of inquiry that was tasked with investigating the events that led to the deaths of the eight during a fitness test.
"No matter how uncomfortable and painful for us as government, we will not hesitate to take corrective and preventative action where it is required," Mchunu told reporters in Pietermaritzburg.
"Therefore I will not hesitate to acknowledge the grave errors that led to this tragedy."
Mchunu said that the department had no regulations of its own related to the carrying out of fitness tests.
Negotiations must still happen
The commission had recommended compensation to the families of the victims as well as disciplinary procedures to be undertaken against four transport department officials.
Mchunu said negotiations with the families over compensation still had to be undertaken.
The report had also recommended investigations against some officials for submitting fraudulent minutes of a meeting to the commission.
The eight people died when they took part in a 4km run at Pietermaritzburg's Harry Gwala stadium in December 2012.
This formed part of a fitness test for Road Traffic Inspectorate job applicants. More than 40 000 people qualified to apply for 90 advertised RTI trainee posts.
Of these, 20 000 applicants attended a fitness test on 27 December and a similar number on 28 December.
The report would not be released to the media until the families have had time to examine it.