Lord's Resistance Army rebels are moving from their bases in northern Uganda in compliance with a ceasefire agreement, Ugandan army officials say.
Many LRA fighters were abducted as children
The LRA fighters are meant to assemble in neutral camps in southern Sudan in terms of a truce with the government.
Some have already arrived in Sudan. The development is being seen as a positive sign that the ceasefire will hold.
Thousands have died during the 20-year conflict in northern Uganda, and more than one million have fled their homes.
Under the terms of the ceasefire agreement LRA fighters - including hundreds of child soldiers - have been guaranteed safe passage to two assembly points in southern Sudan.
On the move
"They are moving," Ugandan army spokesman Major Felix Kulayigye told Reuters news agency.
"We have to be patient, but we are on track."
"Many groups have crossed over to Sudan and [on Sunday] in Kalong, Kitgum district, one LRA group that was moving got in touch with an army commander there and asked for food and water," Walter Ochola, the local commissioner in northern Uganda's Gulu district, told the AFP news agency.
More than 1m Ugandans have fled their homes during the conflict
The move by the LRA comes in spite of an accusation last week that the Ugandan army had broken the ceasefire - an accusation that Uganda denies.
Uganda agreed to a truce on condition LRA soldiers assemble in south Sudan.
Political participation, economic development and help for those affected by the war will be discussed at the talks.
There is no news yet on the expected release of women and children held by the LRA and due to be released in compliance with the deal.
The International Criminal Court (ICC) wants the LRA's top officials - among them Mr Kony - to face charges including murder, rape and forcibly enlisting children.
The LRA has abducted thousands of children and forced them to fight since the conflict began.
Against the wishes of the ICC, Uganda offered amnesty to LRA leaders in exchange for an end to the war.