The talks, which are taking place in the southern Sudanese town of Juba, were due to resume on Friday after a three-day break to allow the rebels to mourn one of their top commanders, Raska Lukwiya, who was killed by the Ugandan army at the weekend.
The LRA wrote to the South African government asking it to be a co-mediator in the talks earlier this week. On Wednesday, the LRA’s deputy commander, Vincent Otti, told the BBC that the rebels had questioned the neutrality of the chief mediator, southern Sudanese Vice-President Riek Machar.
However, the Ugandan government rejected the LRA position. Ruhakana Rugunda, leader of the delegation at the talks, said: "The statement that the LRA has once again lost confidence in the mediator and wants the Republic of South Africa to take over is another contradiction.
"The government of Uganda wishes to reiterate its support for the peace initiative being spearheaded by the government of south Sudan. We are convinced that the mediation mechanisms in place are sufficient."
On Thursday, visiting Ugandan members of parliament met Salva Kiir Mayardit, Sudan's First Vice-President and President of the government of southern Sudan in Juba. One of the MPs, Amongi Betty Ongom, told reporters that Kiir assured them his government was impartial and committed to the talks.
According to Ongom, Kiir also said he had contacted various governments to lobby for the lifting of an indictment by the International Criminal Court against LRA leaders.
"Kiir pledged his personal support and that of his government in protecting the LRA top commanders should they accept to come to Juba," the MP said.
The talks, which began last month, aim to end northern Uganda's 21-year civil war, which has claimed the lives of tens of thousands and displaced nearly two million people.
The LRA is led by Joseph Kony, who believes Uganda should be governed according to the Ten Commandments and claims to be guided by spirits. Thousands of children have been abducted and forced either to fight alongside Kony's troops against the Ugandan army or become concubines to rebel commanders.
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