The fighting erupted during a security operation launched near Eruh, in Siirt province, upon a tip-off that militants from the separatist Kurdistan Workers' Party (PKK) were in the area.
The fighting also left three soldiers wounded, they added.
In a separate incident, three soldiers sustained injuries when their vehicle was fired on as they were approaching a small hamlet in the neighbouring province of Sirnak.
PKK rebels were believed to be behind the incident, the sources said.
Since 1984 the PKK took up arms for self-rule in the mainly Kurdish southeast of Turkey [Turkey-Kurdistan] which has claimed around 45,000 lives of Turkish soldiers and Kurdish PKK guerrillas.
A large Turkey's Kurdish community openly sympathise with the Kurdish PKK rebels.
The PKK is considered a 'terrorist' organization by Ankara, U.S., the PKK continues to be on the blacklist list in EU despite court ruling which overturned a decision to place the Kurdish rebel group PKK and its political wing on the European Union's terror list.
The PKK demanded Turkey's recognition of the Kurds' identity in its constitution and of their language as a native language along with Turkish in the country's Kurdish areas, the party also demanded an end to ethnic discrimination in Turkish laws and constitution against Kurds, ranting them full political freedoms.
Last August, the government announced plans to expand Kurdish freedoms in a bid to erode popular support for the PKK and end the insurgency.
Although the drive faltered amid a ban on the country's main Kurdish DTP party, street protests and PKK violence, Ankara has vowed to push ahead with the reforms.