Bor has been the subject of fighting between the two sides even as peace talks continued in Ethiopia aimed at ending the violence.
The South Sudan army said government forces defeated a rebel force of more than 15,000. South Sudan troops were busy Saturday securing the town and considered a counterattack by the supposedly weakened rebels to be unlikely, the BBC said.
The rebel command had no immediate comment on the statement but the BBC said the rebels could be regrouping.
South Sudan has been in the grip of violence since President Salva Kiira accused his former vice president, Riek Machar, of plotting a coup in the fledgling nation.