Some of the rebels and their leaders are currently believed to be hiding in parts of southern Sudan and the Democratic Republic of Congo (DRC), while others are said to be heading to the Central African Republic
The LRA has insisted it will only participate in peace talks at a new venue and under a different mediation, since it has lost trust in the south Sudanese mediators who brokered the now-stalled talks, and no longer wants to hold them in southern Sudan's regional capital Juba.
It has accused Riek Machar, the chief mediator, of bias - a charge he has repeatedly denied.
"There will be peace in Uganda with or without the peace talks because the peace talks were only good for the terrorists who wanted to get a soft landing"
Yoweri Museveni, Ugandan president
Vincent Otti, the movement's deputy commander, has accused the Ugandan army of violating the truce by attacking his forces in southern Sudan in recent weeks, and vowed to fight back.
But Museveni downplayed the threat, saying the movement had been weakened by a series of army attacks.
"We defeated them and that is why they ran to [DR] Congo. There were no hostilities when they signed the cessation of hostilities agreement," Museveni said.
"There will be peace in Uganda with or without the peace talks because the peace talks were only good for the terrorists who wanted to get a soft landing," he said.
The conflict has raged since 1988, when the LRA under its leader Joseph Kony took leadership of a regional rebellion among northern Uganda's ethnic Acholi minority.
Since then, the conflict has claimed tens of thousands of lives and displaced around a million people.
The rebels have vowed not to sign a lasting peace agreement unless the International Criminal Court lifts an arrest warrant for Kony, Otti and three top commanders for alleged crimes against humanity.