Two mortar bombs hit the UN base in Melut, killing four civilians including a child, who were among more than 1,500 people sheltering there, the UN said. Eight others were wounded.
Melut lies some 35 kilometers west of the main oil production base at Palouch, which rebels are trying to capture.
The United Nations peacekeeping mission in South Sudan (UNMISS) said it "strongly condemns the recent upsurge in fighting".
It was not possible to confirm rebel claims of fighting inside oil fields nor their reports of having killed scores of soldiers, which the government has dismissed as "lies".
More From This Section
Rebel spokesman James Gadet Dak on Tuesday ordered oil companies to evacuate staff and said they were fighting to take the oil zones in Upper Nile to "deny Salva Kiir from using the oil revenues to perpetuate the war".
South Sudan, which won independence from Sudan in 2011 to become the world's youngest nation, once saw 95 per cent of the government's budget come from oil revenues.
Oil companies include China National Petroleum Corp, India's Oil & Natural Gas Corp and Malaysia's Petronas.
Oil fields in neighbouring Unity state, where the government is advancing on a rebel enclave, have almost all stopped pumping due to fighting.
Information Minister Michael Makuei late yesterday dismissed rebel claims of capturing key oil areas and said the production had not been affected.
Government troops launched an assault in late April, one of the heaviest offensives yet in the civil war, which has cut off over 650,000 from aid and seen gunmen raping, torching towns and looting relief supplies, according to the UN and aid agencies.
"UNMISS is deeply concerned by the overall escalation of the conflict, and once again calls on the government and opposition leadership to immediately cease all hostilities and resume negotiations," the UN said.