The latest attack is the largest since rebels called a transport blockade to protest the king's power grab earlier in the month.
"At least three dozen Maoists are feared to have been killed in fierce clashes with the security forces," said a statement on Friday from the army's western divisional headquarters in Kathmandu.
"Between Thursday and Friday, the two sides were engaged in fierce clashes at five different areas in Kailali district," the statement said.
More than 11,000 lives have been lost in the conflict pitting government forces against the Maoists who are battling to oust the monarchy and install a communist republic.
In the latest clashes, 400 rebels attacked forces operating in the village of Hasulia, the army statement said.
Three soldiers and a policeman were killed in a separate clash in Pathariya in western Nepal on Friday and an undisclosed number of injured soldiers were airlifted to Kathmandu for treatment, it added.
King Gyanendra, who seized power, declared emergency rule and sacked the government on 1 February for what he said was its failure to deal with the Maoist insurgency, has offered unconditional peace talks with the rebels.
The guerrillas have responded by imposing an indefinite transport blockade on the Himalayan outpost until they say the king restores fundamental rights to the people and releases his grip on power.