Peace talks between the rebel Lord's Resistance Army and Uganda's government have resumed in Juba in southern Sudan.
Joseph Kony is wanted by the ICC for war crimes
The talks were adjourned as the LRA requested a mourning period for an officer killed a week ago.
A Ugandan spokesman rejected an LRA request that South Africa help mediate, saying he trusted the current mediator, south Sudan's vice-president.
The talks have been greeted as the best chance of ending a 20-year war in which thousands have died or been abducted.
"We respect South Africa's experience in conflict resolution but we do not see the urgency of involving new people given the progress we have made," Paddy Ankunda, the government delegation spokesman, told AFP news agency.
"We feel confident in the mediation of (south Sudanese vice-president) Riek Machar," he said.
End of mourning
Talks are proceeding in a hotel in Juba.
"Today has marked the end of mourning of our slain commander killed by the Ugandan forces in cold blood," LRA spokesman Obonyo Olweny told Reuters news agency.
"We have come back for negotiations and we are also ready for face-to-face interaction with the Ugandan government."
The LRA has declared a unilateral ceasefire but Uganda insists that a comprehensive peace agreement - with the rebels providing details of their forces and deployment - needs to be in place before a ceasefire can be agreed.
Ugandan President Yoweri Museveni has set a 12 September deadline for thrashing out a final peace deal.
The government also wants a guarantee the LRA will not use the halt in fighting to reinforce its positions.
International Criminal Court wants the LRA's top officials - including leader Joseph Kony - to face charges including murder, rape and forcibly enlisting children.
Against the wishes of the ICC, Uganda has offered amnesty to LRA leaders in exchange for peace talks.
The LRA has abducted thousands of children and forced them to fight since the conflict in began.