Vincent Otti, the LRA's deputy leader, said that lifting the International Criminal Court (ICC) indictments against himself and other top LRA leaders was a pre-condition to a full peace deal.
"Lifting the indictments of the ICC is the first condition, because without that one we cannot go back home, because it might be a trap," Otti told reporters from a clearing on the Sudanese-Ugandan border.
However, he then said: "We are going to talk peace, we are going to sign [a comprehensive peace deal], then wait for the indictments to be taken off."
The appeal was rejected by Yoweri Museveni, Uganda's president, who said the LRA should surrender first. He warned rebel leaders they would face death unless they ended their insurgency.
The LRA launched one of the world's bloodiest insurrections from northern Uganda 20 years ago, killing civilians and often slicing off victims' lips and noses.
It is also accused of abducting tens of thousands of children for use as soldiers and sex slaves.
"The ICC indictments have to continue until the LRA leaders fully embrace the peace talks," said Museveni.
"You have to give safety to Ugandans first. If you don't do that, you will die," he said in a warning to LRA leaders.
Women and children
When asked about the release of women and children, as stipulated by the United Nations, Otti said: "We are not going to release our children back home, leaving their parents in the bush. We shall all go back home together."
A truce deal signed last month said the LRA had to be in two camps by Tuesday but Uganda's government has indicated the deadline and alleged ceasefire violations would be reviewed later this week.
"The way forward will depend on the general feeling," said Ruhakana Rugunda, leading the government's negotiating team.
Museveni initially urged the ICC to issue warrants for the LRA, but is now offering amnesty if a peace deal is struck.
However, he has said the government would only push for the ICC to drop its investigation after the rebels leave the bush.