"We shall hit them," Major Felix Kulayigye, a Ugandan army spokesman, said.
"Any attempt to come back to northern Uganda would be taken as a resumption of war."
Fears of renewed war
Aid agencies fear the LRA - one of Africa's most feared rebel groups - could wreak havoc on a Ugandan population traumatised by war if they went back to Uganda.
LRA fighters are notorious for killing civilians, mutilating victims and abducting children.
A landmark truce signed in August had raised hopes of an end to a two-decade civil war that has killed tens of thousands and displaced 1.7 million.
The truce renewed in November gave the rebels until the end of January to gather in two places in southern Sudan - on the borders of Uganda and the Democratic Republic of the Congo, near LRA leaders' jungle hideouts.
The LRA's comments came days after they said they would not resume talks in the south Sudanese capital, Juba, because of concerns for their security after Omar Hassan al-Bashir, the Sudanese president, vowed to "get rid of the LRA from Sudan".
Faltering peace process
The stop-start peace process has faltered in recent months, with both sides accusing each other of violations and the LRA accusing mediators in south Sudan's government of failing to stop the Ugandan army attacking them in Sudan.
LRA spokesman Olweny said the group east of the Nile who were supposed to meet near the Uganda border would probably go back to Uganda.
"They know they can't stop us going back. If necessary we shall use our firepower," Olweny said.
But he added the LRA high command had not yet issued a final order sending the fighters back.
LRA commanders were unavailable for comment.
Some observers believe that the LRA's latest statements are designed to increase pressure on the International Criminal Court to drop war-crimes charges against them.