Turkish attack helicopters fired at Kurdish rebel positions in southeast Turkey Monday.
The fighting came after state media reported that troops surrounded about 100 Kurdish rebels in a mountainous region near the border with Iraq.
The official Anatolia news agency said Turkish forces trapped the rebels in the province of Hakkari by blocking their escape routes to bases in northern Iraq.
Turkey's foreign minister says all options remain open in the fight against Kurdish rebels and terrorists based in northern Iraq.
In an interview with the BBC, Iraqi Foreign Minister Hoshiyar Zebari warned about "disastrous consequences" if Turkey launches an incursion into northern Iraq to pursue the rebels with the Kurdistan Workers' Party, or PKK.
At least two Turkish soldiers were reported killed Monday, including one by a land mine believed to have been planted by rebels in the eastern province of Tunceli, far north of the Iraqi border.
The developments came as Turkey celebrated its 84th anniversary as a republic, with tanks and other military machinery displayed at a national day parade in Ankara.
The Turkish military says it killed 15 Kurdish rebels in fighting Sunday in Tunceli. Turkey accuses Kurdish rebels of using bases in northern Iraq to launch attacks into southeastern Turkey.
The European Union and the United States are pressing Ankara not to invade northern Iraq to pursue the rebels.