Fresh clashes broke out around South Sudan's second-largest city of Malakal on Tuesday, a rebel spokesman and a government official said, the latest turn in the struggle for the capital of the oil-producing Upper Nile region.

The United Nations said Malakal, on the banks of the White Nile near the country's northern border with Sudan, was largely deserted after civilians fled the fighting.

"The rebels had been trying to provoke the SPLA all this time because the SPLA has been given instruction not to wage offensives against the rebel forces," said military spokesman Colonel Santo Domic Chol, using the acronym for the military, known as the Sudan People's Liberation Army.

"This is in line with the call by the president for the national dialogue," he added, referring to a presidential directive on dealing with the rebels.

But rebel spokesman William Gatjiath Deng said government troops launched several attacks on rebel positions early on Tuesday.

"In the fight this morning, Juba regime suffered heavy losses in human and material, as bodies of the Juba regime soldiers lie everywhere," he said in a press statement.

Neither Chol nor Deng had casualty figures.

Civil war broke out in 2013 in South Sudan after President Salva Kiir, an ethnic Dinka, fired his deputy president, Riek Machar, from the Nuer ethnic group.

An internationally brokered ceasefire returned Machar to his position but broke down in July after a gunfight between the two sides in the capital. Machar and some of his fighters fled the country on foot in August, pursued by helicopter gunships.

Sporadic fighting between the rebels and government forces broke out in Malakal a week ago, forcing officials to close the airport. On Friday, Chol told Reuters that 10 rebels had been killed in fighting in Ditang, near Malakal.

The area around the city is a stronghold of Johnson Olony, a militia leader from the Shilluk ethnic group who was appointed an army general when he agreed to join the government in 2013. In April 2015, he announced he was deserting the military to join the rebels.  

The civil war has driven more than 3 million people from their homes. (Reuters)