The latest round of talks seen by both sides as the best chance in decades of ending a war which has wracked northern Uganda and surrounding countries for more than 20 years.
Captain Barigye Bakoku, the spokesman for the Ugandan delegation, said: "I did not see any tension and I hope we are going to move smoothly up to the end because I saw seriousness in both delegations.
"Tomorrow we are going to start on comprehensive solutions and we will move on to other items on the talks' agenda."
Martin Ojul, the head of the LRA delegation, said: "We are here to solve problems... Our expectation is things will go smoothly."
Reinforcing the international drive for peace, mediators from South Africa, Kenya, Tanzania, the Democratic Republic of Congo and Zambia also attended, along with Salva Kiir, the president of Southern Sudan, and Western diplomats.
|The Lord's Resistance Army is active |
mainly in northern Uganda
Talks between the LRA and Uganda began in mid-2006 but broke down three months ago when rebel delegates walked out, saying they were afraid for their safety.
One of the main sticking points in the talks are the warrants issued by the International Criminal Court against several senior LRA leaders.
The rebel leaders say the charges must be dropped before they make peace; the Uganda government says it will ask the ICC to grant an amnesty - but only after a peace deal is signed.