The attackers were suspected members of the Shining Path group, which led a nearly two-decade rebellion until its leadership was captured in the early 1990s.
Some members of the group are still active and have lately grown bolder in their attacks in the country's main coca farming regions.
Yehude Simon, the prime minister, described Thursday's ambushes as "desperate responses by the Shining Path in the face of advances by the armed forces" in the Apurimac Ene valley northwest of Ayacucho.
"I have no doubt that in the next years this zone will be free of leftover terrorists," Simon said.
A surge in rebel violence last year prompted an army offensive in Apurimac Ene.
Authorities accuse the Shining Path of involvement in the drug trade, and of using the profits to fund its cause.
The Shining Path attempted to overthrow the government and install communist rule in the 1980s and 1990s.
Alberto Fujimori, the president during the time of the government crackdown on the group, was sentenced to 25 years in prison this week for his role in crimes committed by an army death squad during his 1990-2000 rule.
Peru's civil war between the government and various Maoist rebel groups, most notably the Shining Path, is estimated to have left at least 70,000 dead.