State radio said on Wednesday the clash was Nepal's deadliest since guerrillas ended a ceasefire last month.
"The bodies of 35 Maoists have been recovered. Three army men are dead and some others are injured," state radio said.
However, an army official, speaking on condition of anonymity, said 44 Maoists and six soldiers were killed in the operation in Rolpa district, 460 km west of the capital Kathmandu.
He said the toll in the clash could rise past 100 and the army had fired from a helicopter to break down Maoist defenses.
A police officer said troops and police raided a suspected Maoist hideout from three sides on Wednesday morning on suspicion that senior rebels were there.
The army official described the hideout as a "fortress" surrounded by sandbags and stones to protect it from attack.
Tolls from clashes in Nepal are difficult to verify independently as they usually occur in isolated areas.
Rolpa is a rural district where the Maoists in February 1996 declared their "people's war" to topple the monarchy.
The rebels ended a seven-month ceasefire on 27 August.