The battle, at Bangui Base, lasted between 13 and 18 hours, Shoke said.
Thirteen SA soldiers have been confirmed dead but there is a 14th body which has not yet been identified. The body might be that of a missing SANDF soldier.
Shoke says the rebels eventually came with a white flag and negotiated surrender.
Twenty-seven South African soldiers were wounded in clashes with rebels who captured the capital Bangui over the weekend, President Jacob Zuma said on Monday.
"During the battle 13 of our soldiers fell, one is unaccounted for," said Zuma.
South Africa deployed 200 soldiers to Central Africa in January to support the poorly trained, ill-equipped government troops following an offensive launched by the Seleka rebel coalition in early December.
"Our soldiers paid the ultimate price in the service of their country.... we honour them," said Zuma.
"Just over 200 of our soldiers fought bandits who wanted to cause harm... but the actions of these bandits would not deter us from from our mission of peace and security," said Zuma.
The rebels renewed their offensive last week and seized the capital Bangui on Sunday, forcing President Francois Bozize to flee the country.
"As a member of the African Union, South Africa rejects any efforts to seize power by force," Zuma told reporters.