Yoweri Museveni, the Ugandan president who arrived in Juba on Monday for what was meant to be a ceremony to ink the peace deal, accused Kony of not being serious about the talks.
"I have come prepared to sign the agreement, but Kony has not showed up," Museveni said. "It is clear that Kony is the one who is not serious."
He suggested that Ugandan forces could abandon a ceasefire that expires on April 16 and resume military operations against LRA rebels who have allegedly been attacking civilians in south Sudan.
"We have the means to act together with them [south Sudan] to solve some of these problems," Museveni said.
Twenty years of fighting have left tens of thousands dead and displaced two million people, mainly in northern Uganda.
Several thousands have also been killed in southern Sudan, where the LRA has camps.
A ceasefire was struck in August 2006, leading to a year and a half of negotiations up to the Juba talks.
Kony, a semi-literate former altar boy, took charge in 1988 of a regional rebellion among northern Uganda's ethnic Acholi minority.
Since the signing of a truce almost two years ago, the war-scarred nation has engaged in aggressive reforms to attract investors and revamp its image.