Two other soldiers were wounded after the missile hit close to a military base in Hakkari province, the private Dogan news agency said.

The agency blamed the attack on the outlawed Kurdistan Workers' Party (PKK), which has been waging an insurgency against the Turkish state since 1984.

Since then, over 40,000 people have been killed.

The PKK is blacklisted as a terror organisation by Ankara and its Western allies.

The deaths come a day after the army said one Turkish soldier was killed in an attack by the "separatist terrorist organisation" -- Turkey's official term for the PKK -- in the eastern province of Agri.

Following the collapse of a two-year ceasefire in 2015, fighting has intensified between Turkish security forces and the PKK in the southeast.

The Turkish military regularly conducts air raids against PKK militants who have bases in the Qandil mountain area of Iraq.

Turkish ground troops also sometimes stage incursions into the area.

Ankara on January 20 launched a cross-border operation in northern Syria against a Syrian Kurdish militia which Ankara says is a "terrorist" offshoot of the PKK.