It said a group of Maoists opened fire on a security patrol in the forests of Rupandehi district on Sunday, 300 km west of Kathmandu, the capital.
"We have recovered 16 bodies of Maoist rebels. The search operation is continuing," an army officer, who declined to be named, told Reuters.
He said six soldiers and policemen were wounded in the battle which lasted more than an hour.
There was no immediate comment from the Maoists who are fighting to overthrow the monarchy in the world's only Hindu kingdom.
Witnesses said the fighting had been heavy.
"There was heavy fighting and we could hear the sound of explosions," Sher Bahadur KC, a local journalist, said from Butwal, the nearest town.
The Maoists, who want to set up a republic, have stepped up attacks on security forces since they ended a four-month truce in January after the royalist government refused to match it.
More than 13,000 people have died in the decade-old conflict that has shattered the aid and tourist-dependent economy.
The monarch sacked the multi-party government, seized power in February 2005 and suspended civil rights and media freedom, saying it was necessary to crush the Maoist revolt.