Tens of thousands have already crossed the Nile in boats to escape fighting around rebel-held Bor.
A government military spokesman said the front line continues to shift but it appears fighting is about 45 miles north of Juba, the country's capital.
In Ethiopia, where peace talks are taking place, a spokesman for the rebels said Ugandan helicopters and fighter jets are bombing rebel positions.
As control of certain regions in South Sudan has changed, tens of thousands of residents have fled their homes to escape fighting that often pits the Dinka ethnic group of president Salva Kiir against the Nuer group of Riek Machar, his former deputy who now commands renegade forces.
The violence has displaced 413,000 people, including more than 73,000 who sought refuge in neighbouring countries, says the UN.
Troops from neighbouring Uganda appear to be fighting on behalf of President Kiir.