Brigadier Kolo said he was speaking with the authority of LRA leader Joseph Kony (r)
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Hopes are rising that Uganda's rebels and government could hold talks to end 18 years of conflict, which has led 1.5 million people to flee their homes.
A senior commander of the Lord's Resistance Army (LRA) told the BBC that it wanted to end the conflict through peaceful means.
And the government has extended its ceasefire until next week.
The BBC's Will Ross in Uganda says that both sides now say they are ready to talk, which is a starting point.
Our correspondent says the main challenge is now to build and maintain trust between the two sides.
More than 20,000 children have been abducted by the rebels to become fighters and sex slaves.
UN criticised
Information Minister James Nsaba Buturo said that the truce would now last until Tuesday night - it had expired earlier this week.
"The extension decision shows that the government is entirely committed to the peaceful resolution of the conflict," he said.
Announcing the rebel's commitment, Brigadier Sam Kolo said he was speaking with the authority of LRA leader Joseph Kony.
Thousands of children have been abducted by the LRA
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He also appealed to the government to broaden the area of the ceasefire to cover northern Uganda and southern Sudan.
On Thursday, President Museveni indicated that the ceasefire could be extended indefinitely if the rebels demonstrated a similar commitment.
Brigadier Kolo said talks with former minister Betty Bigombe, who is mediating between the two sides, have been cordial - and he stated that if that spirit is maintained, he believes the conflict can come to a peaceful end.
Following a brief visit to Uganda by a mission from the United Nations Security Council on Thursday, a coalition of local and international organisations has strongly criticised the mission for not focusing attention on northern Uganda.
Some civil society groups have also accused the army of trying to undermine the peace efforts by highlighting recent rebel attacks.
Ten years ago, a similar peace effort was attempted but did not succeed.
The BBC's Will Ross says that most people in northern Uganda support the idea of peace talks - partly because the LRA force is almost entirely made up of abducted children and also because attempts to end the war militarily have not brought a lasting peace.