The change of heart follows a trip on Sunday by the Joaquim Chissano, the former president of Mozambique and UN envoy for the conflict, to talk with Joseph Kony, the fugitive rebel leader.
Uganda said it had wooed LRA delegates in return for the addition of mediators from African countries besides south Sudan.
The insurgency, led by fighters notorious for mutilating victims and kidnapping children, has killed thousands of Ugandan civilians and displaced nearly 2 million people.
Olweny said the promise to expand the mediators to include five other countries – Kenya, Tanzania, South Africa, Mozambique and the Democratic Republic of the Congo – satisfied the LRA.
But the LRA demanded better security for their negotiators in Juba and their fighters scattered in south Sudan and on the Sudan/Congo border.
"If those concerns are addressed, we can go back," he said.
The LRA accuses the Ugandan army of ambushing their fighters in Sudan. A truce agreed between the two sides in August expired last month with no renewal.
"They [Uganda] should pull their troops out of Sudan. Only when the last troop crosses back to Uganda can we have peace," Olweny said. He said that was not necessarily a pre-condition of talks restarting.
The army insists it will stay in Sudan to monitor the LRA.