Ugandan President Yoweri Museveni says a three-month operation in Democratic Republic of Congo against the LRA has captured just a fifth of the force.
He told the BBC that 90 Lord's Resistance Army (LRA) rebel fighters had been held in the joint offensive.
Speaking on a visit to London to attend Commonwealth Day celebrations, he said pursuing LRA leader Joseph Kony was like "hunting a cockroach".
Uganda, DR Congo and Sudan launched the joint offensive in mid-December.
Ugandan troops were supposed to have finished their operation in DR Congo by the end of February, but last week it announced agreement had been reached for them to continue their pursuit of the rebels.
Mr Museveni refused to confirm for how long his troops have been granted leave to remain on Congolese soil, promising a statement next week.
Congolese President Joseph Kabila has reportedly come under pressure from some of his supporters to get the Ugandan troops out.
The Ugandan president told the BBC's Focus on Africa programme it was a campaign of attrition and promised Mr Kony would eventually be caught.
"When you are dealing with this type of group, you are not fighting - it is more like hunting," he said.
"When you are hunting... a cockroach, its best weapon is flight and concealment. Our aim is to counteract those. We have caught 90 [rebels]. That is almost one fifth of their whole group."
Last week, Uganda's military paraded on TV an LRA commander - believed to be fourth-in-command - who was captured in north-eastern DR Congo. But Mr Kony has remained elusive.
"There is no mistake. Kony will be caught - just like we caught his number four. That's how these people end up," Mr Museveni said.
"We have killed many of his people. You must have heard of the word 'attrition'? That attrition is going on all the time."
Mr Kony launched his brutal rebellion against the Ugandan government more than two decades ago.
It has left tens of thousands of people dead, driven some two million people from their homes and destabilised a swathe of central Africa.