Al Jazeera's Yvonne Ndege, reporting from the border between Sudan and the Democratic Republic of Congo (DRC), said that Kony and the other commanders wanted further details of the agreement which would see him tried in Uganda rather than by the International Criminal Court (ICC).
"Kony wanted to know what the Ugandan high court will do with him after the peace deal is signed," Ndege said.
Joseph Kony is the head of the Lord's Resistance Army (LRA), which has waged a 20-year war against Uganda's government.
Tens of thousands of people were killed and two million others displaced by fighting in northern Uganda.
Kony was a former altar boy and wants the country to be ruled according to the Bible's 10 commandments.
Kony belongs to the Acholi ethnic group and was born in Odek, in Uganda's northern Gulu district, in the early 1960s.
The LRA signed a peace deal with Kampala in July 2006, paving the way for peace talks in the South Sudanese capital Juba.
He refused to participate in talks, citing fear of arrest over a warrant issued by the International Criminal Court (ICC).
The self-proclaimed prophet has only appeared in public twice since the peace talks with the Ugandan government began.
"He also wants to clarify whether traditional forms of Ugandan justice will be implemented. If it is, it will essentially allow him to walk free."
David Matsanga, the chief LRA mediator, told Al Jazeera that he has resigned from his post.
"Kony was no where near the area in which the talks took place. He has constantly postponed negotiations, despite his assurances that he will turn up today."
"I am tired of this situation, it is extremely frustrating. I promised myself that if Kony violates another agreement to hold talks, I will resign."
The ICC indicted him in 2005 for war crimes and crimes against humanity and continues to insist he must be tried in The Hague.
If signed, the peace agreement would have put an end to a 21-year conflict between the Lord's Resistance Army (LRA) and the Ugandan government.
Yoweri Museveni, the Ugandan president, is due to sign the deal separately on Sunday.
Ruhakana Rugunda, the Ugandan government's chief negotiator, said the delay was no big deal.
"Long-lasting peace in northern Uganda is what we want, and we won't be derailed by a time schedule," he said.
The agreement between the government and the LRA is vague on disarmament and the release of the hundreds of children and women, still believed to be in LRA captivity.
Twenty years of fighting have left thousands of Ugandans dead and displaced two million people, mainly in the north of the country.
Several thousands people have also been killed in southern Sudan where the LRA was once based.
A ceasefire was agreed in August 2006, paving the way for peace talks in Juba, Sudan, that have lasted more than a year and a half.
However, even with an agreement, Kony is not expected to return to the Ugandan capital Kampala.