Beeld reported on Tuesday that beyond the official toll of those injured and killed, six special forces operators were also killed in the fighting.
SANDF spokesperson brigadier general Xolani Mabanga said the soldiers' remains arrived by 8pm on Tuesday.
He said details of a military receival of mortal remains ceremony would be announced on Wednesday. The families would then decide whether they wanted military funerals for their loved ones.
Earlier, the SANDF released the names of the 13 soldiers killed in CAR.
It said corporals Mokgadi Darius Seakamela and Ntebaleng Andrew Mogorosi, as well as lance corporals Daniel Sello Molara and Lukas Mohapi Tsheke were among those killed on Sunday.
The riflemen killed were: Lesego Maxwell Hertzog, Zamani Jim Mxhosana, Xolani Dlamini, Vusumzi Joseph Ngaleka, Karabo Edwin Matsheka, Khomotso Paul Msenga, Maleisane Samuel Thulo, Motsamai William Bojane, and Thabiso Anthon Phirimana.
All of those killed were members of One Parachute Battalion from Bloemfontein.
"In addition, the SANDF would like to report that the member who was reported missing in action has been found alive and is in good spirit[s]," the SANDF said in a statement.
Held captive
Apart from those killed, 27 SANDF members were wounded when more than 200 South African soldiers fought an armed force of about 3 000-strong.
Mabanga said he could not verify rumours that around 40 troops were being held captive by rebels in the CAR.
"We have not heard of that," he said.
Mabanga said on Tuesday morning the CAR rebels regretted the action that led to the deaths of the South African troops.
"On Sunday morning the leaders of the rebels came to the base and discussed what happened on the ground and they regretted exchanging fire with SANDF soldiers," he said.
"Since then, there hasn't been any threatening situation against the SANDF. We are not taking anything lightly and are taking all precautionary measures to ensure SANDF members are safe on the ground."
Special forces killed too
Mabanga said the SANDF did not receive any instructions regarding troop movements and could not comment on media reports alleging what happened on the ground.
"We cannot comment on reports by the media based on allegations," he said.
Further to the allegations of more deaths of South African soldiers, Beeld reported that the SANDF became a target for reportedly helping CAR President Francois Bozizé flee the country into the Democratic Republic of Congo.
According to the report, top structures were warned by senior SANDF officers last week that the CAR mission amounted to "suicide".
South African Air Force aircraft were also put on standby on Monday night, although due to financial constraints the Gripens were not armed with weapons with an attack capacity.
SANDF soldiers reportedly struggled on the ground due to a lack of logistics and air support.
Soldiers had to ask French parachutists for essential equipment. There was only one doctor present with a backpack for medical support.
'Disaster'
The report also stated that renewed fighting broke out on Monday between SANDF soldiers and rebels.
The Democratic Alliance (DA) said on Tuesday that new reports on the "disaster" in CAR showed the need for a parliamentary inquiry.
"The SANDF soldiers evidently acquitted themselves well under fire, in circumstances where they were vastly outnumbered by rebel forces," said DA defence spokesperson David Maynier in a statement.
"But in the end, they appear to have been left dangling, without the necessary military support. We need to get to the bottom of why the SANDF was deployed in the CAR, effectively to support President Francois Bozizé."
He said it also needed to be known how the 13 soldiers died in the CAR.
The DA had written to the speaker of the National Assembly Max Sisulu, requesting the establishment of a multi-party ad hoc committee to conduct an inquiry on the SANDF's deployment in CAR.
"In the end, President Jacob Zuma's decision to deploy the SANDF in the CAR – effectively to support President Francois Bozizé – has been a complete disaster," said Maynier. – Sapa