A second group would leave on Saturday and the last on Monday, Rolt added.
The troops were supposed to have left on Monday.
Ministerial spokesperson Sam Mkhwanazi said on Tuesday the delay was related to a logistical hold-up, most likely a hiccup in the arranging of over-flight rights for the SA Air Force Boeing 707 aircraft that would be used to transport the troops to Sudan.
On Monday, Colonel Johan van der Walt told parliament's defence committee the departure of the 186 soldiers from the Infantry Protector Company was due to delaying tactics by the Sudanese government.
"But the deployment was delayed because the troops did not have passports and visas, as now required by the Sudanese government," he said.
Mkhwanazi later on Monday denied the Sudanese government were using delaying tactics, saying relations between South Africa and Sudan were good.
Speaking after the committee meeting on Monday, Rear Admiral Edward Ratala, director of operations at the SANDF's Joint Operations Division, said the African Union (AU) had initially been told by the Sudanese government no passports were needed, and visas could be obtained on arrival.
"But now they have confronted us with no-fly zones - not permitting our troops to fly over certain areas - and say they must have visas before departure," Ratala told Sapa at the time.
South Africa was expected to send about 300 troops over the course of this week to the region, he said.
The AU has a mandate to send 3 320 troops from various African countries to the region to "investigate, report and monitor" on events.
Van der Walt told the committee that after numerous visits to the region, he felt the Sudanese government was "turning a blind eye to the atrocities in Sudan".
He said a camp outside the city of El Fasher - AU headquarters, and the provincial capital of Sudan's North Darfur region - was now home to 60 000 refugees.
Most of the South African contingent would be based in the town of Katum, about 200km north-west of El Fasher