The conference came on the same day that he attended talks with a Ugandan government official and Riek Machar, the vice-president of the autonomous government of Southern Sudan, in a tent on the Sudan-Congo border.
The elusive rebel leader is wanted for crimes against humanity and war crimes after the international criminal court issued an arrest warrant for him in 2005.
During the conference Kony, who describes himself as a prophet, denied committing any atrocities and blamed a lack of "good communication to the world" for the bad reputation of his movement.
The Ugandan government and humanitarian groups have accused the LRA of kidnapping children - forcibly conscripting boys and marrying girls to his fighters.
According to UNICEF at least 25,000 children have been abducted.
In response to these claims, Kony said: "I cannot fight with children. There is not any children in position. There is not any abduction in the LRA."
Few outside of his movement - government officials or journalists - have ever met Kony.
Another round of meetings are scheduled for Wednesday.