South Sudan President Salva Kiir on Wednesday called on rebels to resume peace talks as the country marked its third birthday with celebrations overshadowed by fighting that has killed thousands and brought it to the verge of famine.

In a swift response, rebel leader Riek Machar told Reuters in Ethiopia that he was ready to resume dialogue but warned his troops would target South Sudan's oil installations if fighting resumed and the government used oil revenues to buy arms.

Clashes erupted in the capital Juba in December pitting the government forces of Kiir against supporters of Machar, his former deputy and long-time rival. The conflict has reopened deep ethnic tensions in the world's youngest country, which only won independence from Sudan in 2011.

"Put down your guns and come home," Kiir said in Juba during a ceremony marking the anniversary of independence. "I still renew my call upon him (Machar) to accept the logic of peaceful resolution to the conflict so that we resolve this issue."

Peace talks between Kiir and Machar produced few results and stalled after they last met in Ethiopia's capital Addis Ababa in May and agreed on a ceasefire.

"On our side, we are ready to continue negotiations," Machar told Reuters in Addis Ababa, adding that he has also called for the talks to be resumed soon.

"Time is ticking ... We don't want to be blamed."

The mood in Juba was markedly more muted than in 2011 when joyous revellers sheathed in South Sudan flags thronged the streets and danced through the night.

Three years on, a much smaller and more reticent crowd listened as the president gave an independence day address. An ongoing curfew enforced by the army every day at 6 p.m. local time was expected to further curtail any celebrations.

More than 10,000 people have been killed since clashes broke out in December and violence spread to oil-producing regions, slashing output by a third and crippling South Sudan's oil-dependent economy.

The United Nations has warned the east African country faces a catastrophic famine, with humanitarian agencies unable to supply food or medicine to many remote northern regions due to insecurity.

READ: South Sudan famine within weeks without funding

Diplomats from Western powers that helped South Sudan gain independence say neither Machar nor Kiir seem fully committed to the peace talks, with both sides accusing the other of violating previous agreements.

Rebels have accused regional mediators of siding with Kiir's government and want Ugandan troops brought in to support government forces to leave South Sudan.

"These demands will not take us anywhere, let us focus on peace, reconciliation and coming back together," Kiir said, adding that Ugandan troops would stay. "I will not order the Ugandan forces to leave South Sudan until when we are secure and we know that our institutions are being protected."

Oil loans

South Sudan's Finance Minister said last week the government plans to borrow another $1 billion from oil companies to fund its budget and repay debts piled up by previous governments.

Machar, however, said the money will be going to buy arms.

He warned that if fighting resumed, his troops would try to stop production from South Sudan's oil fields - even if United Nations peacekeepers were guarding these installations.

"They are not using it (oil revenue) for service delivery, development like building roads - it is for sustaining its war machinery. So we must deny them use of such resources if there is no peace," Machar said.

"We won't harm oil installations but we will make sure it (output) stops, because it will be used by the government to buy arms."

Machar also asked for South Sudan's oil revenues to be put into an escrow account, to be administered by the international community, until after the conflict is over.