By Carl Odera

JUBA, July 9 (Reuters) - South Sudan's president 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.

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

South Sudan has been in political turmoil since President Salva Kiir sacked his deputy Riek Machar last year, triggering a conflict that has reopened deep ethnic tensions in the world's youngest country which only won independence from Sudan in 2011.

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

"Put down your guns and come home," Kiir said in the capital 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."

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

Three years on, a much smaller and 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 Juba 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 deploy food or medicine to many remote northern regions due to insecurity.

Diplomats from Western powers who 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 regime 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," he said. (Writing by Drazen Jorgic; Editing by Raissa Kasolowsky)