Joseph Kony delivered his comments in a rare interview with Radio France International on Sunday.
"As the chairman of the Lord's Resistance Army I want these peace talks to resume back again to Juba," he said. "I want to go to table back again to Juba and I need also not to fight again with Uganda government."
A delegation from the Lord's Resistance Army had been negotiating with the Ugandan government, under the mediation of Mozambique's former president Joachim Chissano and the vice president of the semi-autonomous government of southern Sudan, Riek Machar. By April, the two sides had drafted a peace agreement, but the talks collapsed after Kony failed to turn up for a meeting to sign the agreement.
Sunday's interview provides Kony's first public comments since the failed meeting.
"My main message to the people of Uganda is this: 'Me, as the chairman of the Lords Resistance Army I am the one who called peace talks, so I am not going to refuse anything about this,'" he said. "And I am agreeing to continue dialogue until we finish everything and I am not going to go back to war with the Ugandan government. "
In response to the apparent failure of the peace process, the governments of the Democratic Republic of the Congo, Uganda, and southern Sudan agreed to launch a joint military operation against the Lord's Resistance Army. The wisdom of the military approach appeared to be bolstered after Lord's Resistance Army rebels attacked southern Sudanese troops earlier this month.
But southern Sudan's Riek Machar says he is willing to resume negotiations.
"This is a good step forward that he has come out to say he would want the peace process to continue," he said. "I am looking to receive a call from him. Already the leader from his team has rang me in the morning and I told him that once General Joseph Kony rings me we will make the arrangements for him to come to Juba."
Ugandan military spokesman Paddy Ankunda said he also welcomed the resumption of peace talks.
"What we want is peace. If he can gives us a shortcut by accepting to sign the agreement that is welcome," he said. "We will wait and see. If he is serious he will turn up, if he is not, he will not. He had better come himself, but if he can give us any authentic mediators or delegates we will work with whoever can take us to that signature."
Joseph Kony and his top deputies are wanted by the International Criminal Court for war crimes. The two-decade conflict has spread from Northern Uganda into Sudan, the Democratic Republic of Congo and the Central African Republic.