The agreement was signed late Monday in the provincial southern Sudanese town of Juba where the two sides have been holding talks for the last 19 months.
"We have agreed that severe crimes committed by the LRA during the war will be tried under a special division of the High Court in Uganda," said Captain Chris Magezi, the spokesman of the government delegation.
The rebel group is holed up a hideout in north eastern Democratic Republic of Congo.
More than half of its fighters are believed to be composed of children abducted from northern Uganda.
"Less severe crimes can be dealt with using Mato Oput, (a traditional reconciliation mechanism by the Acholi people of northern Uganda) of ever junior courts," Captain Magezi said.
But rebel leader Joseph Kony and two of his commanders are wanted in the Hague-based International Criminal Court for war crimes and crimes against humanity.
The LRA has vowed never to sign a final peace deal unless Kampala can persuade the World Court to drop the case -- something analysts say is unlikely.
The LRA, notorious for brutal attacks against civilians such as burning them to death and hacking their limbs off, said they may accept local courts but warned the government not to make unilateral decisions.
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