He said a separate signing ceremony for Yoweri Museveni, the Ugandan president, which had been planned for Tuesday in the south Sudanese capital Juba had been indefinitely postponed.
Elders in northern Uganda tried to meet Kony in order to salvage the fragile peace deal, but the peace talks appeared close to collapse.
Kony failed to turn up in the jungle town of Ri-Kwangba on the Sudan-Congo border to sign the agreement and his chief negotiator subsequently quit.
David Matsanga said he had not spoken to Kony in four days and suggested Kony might never have meant to make it for the signing.
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.
"Kony keeps lying to me and saying he'll come to meet us and then he doesn't come to meet us," said Matsanga.
LRA fighters and negotiators had gathered in a jungle clearing waiting for Kony to emerge from hiding and sign a deal to end the two decade-long northern Uganda insurgency.
But then Riek Machar, South Sudan's vice-president who has chaired the talks since mid-2006, said Kony wanted clarification on how the government will address atrocities charges against him and other rebels.
Kony, who is wanted for multiple war crimes by the International Criminal Court (ICC) in The Hague, "still wants these issues explained to him - that is why we have delayed", said Machar.
Al Jazeera's Yvonne Ndege, reporting from Nbanga in Southern Sudan, said the negotiating teams had "effectively disintegrated".
"We understand that three or four representatives of the LRA have walked into the bush to try and talk to Kony over a phone line," she said.
"The UN, the African Union and representatives from other organisations are walking around the camp that I'm in scratching their heads trying to cook up a 'plan B'.
"On top of that, there are more than 100 delegates representing all sorts of organisations wondering just how on earth they are going to get out of here ... shambolic and confusing would be a generous description of the situation."
Decades of conflict
The two-decade long conflict between the LRA and Ugandan government has killed tens of thousands of people and uprooted two million others in northern Uganda.
It has also destabilised neighbouring parts of southern Sudan and eastern Congo.
ICC prosecutors accuse Kony and two of his deputies of crimes including rape, murder and the abduction of thousands of children to serve as fighters, porters and sex slaves.
As part of the final deal, Uganda had agreed to approach the ICC and request that the indictments be withdrawn, though any decision to drop the international charges would have to be approved by judges at the court.
Even if Kony does sign a final peace deal, the rebels have vowed never to disarm until the indictments are scrapped.