Former South Sudan vice-president Riek Machar says his troops have seized an oil-producing area and now control much of the country.
More than 500 people have died in the past week since President Salva Kiir accused Mr Machar of staging a coup attempt.
Mr Machar told the BBC that the forces fighting the government were under his command.
Oil accounts for more than 95% of the country's economy, and the state, Unity, which Mr Machar said his forces have captured, produces much of South Sudan's oil.
The former vice-president said he was prepared to negotiate with the government if politicians arrested earlier this week after the coup attempt was announced were released.
His comments came as several US military personnel were wounded when their aircraft came under fire while evacuating US citizens from Bor the capital of eastern Jonglei state.
A US military statement said three CV-22 Ospreys were attacked as they approached Bor, which is occupied by forces loyal to Mr Machar.
Four wounded military personnel were treated in Nairobi, Kenya, and were in a stable condition.
Jonglei state has seen some of the worst violence since South Sudan became independent from Sudan in 2011, with hundreds killed in periodic clashes between rival heavily-armed ethnic militias.
Reuters reports that the African Union is calling for a ceasefire and that in a statement, it described the killing of UN peacekeepers and civilians at a UN camp as a war crime.
Fighting that began on Sunday in the capital Juba has swiftly spread to other parts of the country, fuelled by ethnic divisions between the main Nuer and Dinka tribal groups.
The African Union said in a statement that its chairwoman, Nkosazana Dlamini-Zuma "calls for an immediate humanitarian truce for the Christmas season, as a sign of a commitment by all concerned to the well-being of the people of South Sudan".
Hospitals working around the clock, says nurse
A New Zealand nurse working in the South Sudan capital of Juba says staff in the city's two hospitals are working round the clock to deal with hundreds of casualties in the wake of fierce fighting in the country.
The International Red Cross says thousands of people have fled their homes seeking safety from the violence.
It says it is providing Juba's hospitals with support to cope with the influx of patients, including wound-dressings and other urgently needed medical supplies.
New Zealander, Felicity Gapes, who is leading the medical response in Juba on behalf of the Norwegian Red Cross, says hospital staff are struggling because of the sheer volume of patients and the severity of the injuries.
She says staff know there are more people who need care, but they are having problems reaching health-care facilities because of the security situation and the lack of available transport.
The Ministry of Foreign Affairs and Trade is warning New Zealanders against travel to South Sudan, citing armed conflict, civil unrest, terrorism and violent crime.
It says the country poses an extreme risk for travellers and any New Zealanders there should leave, while any New Zealander travelling there should register with the ministry.
It has warned against all travel to within 40 kilometres of South Sudan's northern border with Sudan, citing border disputes and inter-tribal clashes.
The ministry says outside the capital city of Juba, the country is lawless, and the government's ability to help New Zealanders in trouble is severely limited as there is no diplomatic presence in the country.
It says there are six New Zealanders in Sudan.