Irfan Balkanlioglu said the soldiers were shot by PKK militants and two others were injured, Dogan, said. The operation, in Mesudiye district, was continuing.
In another attack, one soldier was killed and six were wounded in clashes with PKK militants in the southeastern province of Hakkari, the army said in a statement.
One soldier was seriously wounded, the army added. The state-run Anadolu news agency reported the clashes occurred in Altinsu district.
The fatalities occurred two days after eight soldiers were killed in fighting with Kurdish militants, the deadliest attack on the military since the failed July 15 coup.