Military spokesperson Lieutenant Colonel Shaban Bantariza said four Lord's Resistance Army (LRA) fighters were shot dead in Pader District on Sunday.
"Then late on Monday we caught up with another group near the River Aswa in Gulu and killed 12 of them," he added.
For 19 years the cult-like LRA has terrorised isolated communities on both sides of the border with Sudan, uprooting 1.6-million people in northern Uganda alone and triggering one of the world's worst humanitarian disasters.
More than 90 percent of people in the worst-hit areas now live in squalid camps.
The LRA has no clear political goals, but is notorious for targeting civilians and abducting thousands of children as fighters, porters and sex slaves.
Uganda's army says LRA leader Joseph Kony is hiding in southern Sudan, and under a 2002 deal with Khartoum it can pursue him there.
Ugandan troops are only allowed to roam south of the road between the Sudanese towns of Juba and Torit.
But Ugandan military chiefs say Kony, a self-proclaimed prophet, retreated north of this so-called "Red Line" last month, and they want Sudan's government to let them follow him.
"This is what we have been discussing with Khartoum," Bantariza said. "For now, Kony is having an undeserved rest."
The LRA, which is founded on religious symbolism, traditional rites and fear, has never given a clear account of its aims beyond opposing Uganda's President Yoweri Museveni.