The rejection has dealt a potential blow to negotiations aimed at ending a 20 year old conflict.
Despite an offer from the Ugandan government of "total amnesty" for rebel chiefs, the LRA said security issues precluded both LRA leader Joseph Kony and his deputy, Vincent Otti, from attending the talks.
Both men and three other LRA commanders are wanted by the International Criminal Court in The Hague for war crimes.
Mr Otti announced the rebels' refusal on the day the now-postponed peace talks had been due to start in Juba, southern Sudan.
Both Kampala and the autonomous government of southern Sudan, which is mediating in the talks, had been pushing the LRA to send a top-level negotiating team.
Mr Otti told chief mediator Riek Machar, the vice president of southern Sudan, that neither he nor Kony could attend the talks, at least at first, due to security concerns.
They are considered fugitives by the ICC, which issued the arrest warrants against them last year.
Tens of thousands of people have been killed and some two million displaced in northern Uganda since the LRA took over leadership of a regional rebellion in 1988 in a bid to oust Uganda’s President Yoweri Museveni.
The LRA claims to be fighting to replace Mr Museveni's government with one based on the Bibles’ 10 Commandments.
But it has become better known for atrocities, particularly the kidnapping of an estimated 25,000 children, girls who have been made sex slaves and boys enlisted as fighters.
Otti will “come later”
"I cannot come at this time. Can I risk myself going to Juba?" Mr Otti told Mr Machar.
The two met at a remote jungle clearing on Sudan's border with the Democratic Republic of Congo (DRC), where the LRA leadership is based.
Mr Machar, who had been waiting at the undisclosed location for four days in the hope of making a personal appeal to Kony, was clearly frustrated with the rebel stance, which he said would delay the talks until at least Friday.
"Yes, you can (go to Juba) if you love your country," he replied, according to an AFP correspondent at the scene. "What stops you from coming to Juba?"
Mr Machar said the LRA stance jeopardised the credibility of his own government, which has been criticised for meeting the LRA in light of the war crimes charges levelled at them by the ICC.
"We defied the whole world so you could have a chance to come and say your viewpoints," Mr Machar said.
"I will come later," Mr Otti said, prompting another rejoinder from Mr Machar, who reminded the LRA number two that Mr Kony had to be present to sign any peace deal.
"If there is a peace agreement, you know Joseph must sign it," Mr Machar said.
Mr Otti insisted Mr Kony would sign a deal if one was reached. "The time will come," he said. "A year or a month. But Joseph Kony will sign or there is no peace."
In the meantime, Mr Otti said the LRA would send two senior colonels – Bwone Lobwa and Santo Alit -- to join the rebel delegation to the talks in Juba.
There was no immediate reaction to that move from Ugandan officials, who had made no secret of wanting Mr Kony or at least Mr Otti present.
The Ugandan government argues that they are the only people among the rebels who have the authority to negotiate.