A total of "43 new bodies were found," bringing the provisional death toll from Friday's attack in Oudalan province to 51 soldiers, the army said in a statement.
Earlier it said eight soldiers had been killed.
The attacks took place on Friday in Deou and Oursi in Oudalan province, it said in a statement.
Eight soldiers were killed, three were wounded and several are missing, it said, giving a provisional toll.
"Around 60 terrorists were killed in an airborne counterattack targeting enemy columns that were trying to escape toward the border in the north" toward Mali, it said.
"Seven armed vehicles and dozens of motorbikes were also destroyed."
The statement urged against publicizing unofficial tolls until casualties were confirmed on the ground.
Burkina Faso is battling a jihadist insurgency that spread from neighboring Mali in 2015.
The violence has led to more than 10,000 deaths, according to estimates by NGOs, and displaced some two million people.
Anger within the military at failures to stem the bloodshed led to two coups last year.
Attacks have mounted since the start of the year, claiming more than 100 lives in the last two weeks, according to an AFP count.
Insurgent activity has taken place before the departure of French forces from Burkina Faso. Paris has decided to relocate its Sahel forces elsewhere.