Army spokesman Philip Aguer said troops loyal to President Salva Kiir were battling forces allied to former vice president Riek Machar inside the town of Malakal, capital of Upper Nile state.
He also said troops were preparing an offensive against Bentiu, the main town in oil-rich Unity State, to follow on from their recapture of Bor, another state capital that had fallen into rebel hands during the nearly two weeks of clashes.
"The rebels are still controlling Bentiu but the SPLA is planning to retake Bentiu soon," he added.
The violence in South Sudan, a fledgling oil producer which won independence from Sudan just two years ago, has left thousands dead, according to the United Nations.
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Ten of thousands of civilians have also sought protection at UN bases amid a wave of ethnic violence pitting members of Kiir's Dinka tribe against Machar's Nuer clansmen.
Amid reports of bodies piled in mass graves and witness testimonies of massacres and summary executions and rapes, UN Secretary General Ban Ki-moon has promised those responsible would be "held accountable".
Crude prices have also edged higher because of the fighting as oil production, which accounts for more than 95 percent of South Sudan's economy, was dented by the violence and oil workers evacuated.
Kenyan President Uhuru Kenyatta and Ethiopian Prime Minister Hailemariam Desalegn flew into Juba today for talks with President Kiir, the latest in a line of peace brokers who have made the trip since the fighting began on December 15.