The casualties included 10 Lord's Resistance Army (LRA) rebels, according to reports.
"We killed 10 rebels yesterday, captured six others and recovered nine guns and one solar panel when we attacked a group of about 25 rebel fighters hiding in the bush," army spokesman Paddy Ankunda said on Monday.
He said the battle took place in the area of Loyajonga, 50km east of Gulu town.
Four travellers, who were heading for Sudan, were killed a day earlier at Awino-Luyo in Kitgum district, near the border with Sudan, when rebel suspects ambushed a truck heading for Lubone in southern Sudan.
The nationalities of the four are not yet known.
Independent sources could not be reached to confirm the latest clashes, but Ankunda said the government side did not suffer any casualties because the army used a helicopter to pound the insurgents.
Joseph Kony is the reclusive head
of the LRA
The LRA has been battling government forces since 1988 to replace President Yoweri Museveni's secular regime with one based on the Bible's 10 commandments.
It is accused of killing and maiming thousands of people and displacing 1.6 million others, forcing them to live in squalid camps dotting the entire northern region.