In a televised speech on Sunday, Recep Tayyip Erdogan said: "We have so far tried to handle this issue with patience... to resolve this problem with a democratic approach... [but] these are not acts that one can put up with."
The response came after a week in which 13 members of the Turkish security forces were killed by Kurdish fighters.
The latest clash took place overnight on Saturday in the Siirt province when seven soldiers and one member of the village guard, a government-paid ethnic-Kurdish group supporting the Turkish army, were killed by fighters thought to belong to the Kurdistan Workers' Party (PKK).
The army launched a security operation at dawn on Sunday in response, bombing the area to which the fighters had fled and deploying elite commando teams.
Five soldiers were killed in a landmine explosion blamed on the PKK, on a rural road in Bitlis province on Thursday.
A PKK fighter had also been killed after ignoring calls to surrender during a security operation, a news agency reported on Sunday citing the local governor.
The PKK is listed as a terrorist group by Turkey, the European Union and the United States.
It has fought for Kurdish self-rule in the largely Kurdish southeast of Turkey since 1984 in a conflict that has claimed more than 37,000 lives.
The number of clashes in the region has risen since 2004 when the PKK called off a five-year unilateral ceasefire.
At least 85 Kurdish fighters and 49 members of the security forces have been killed this year in the southeast and Kurdish groups have claimed responsibility for 11 blasts in urban centres, in which nine people were killed and nearly 140 others injured.
In recent months the Turkish army has shifted thousands of troops to areas near the Iraqi border to stop the infiltration of PKK fighters from the mountains of neighbouring northern Iraq.
Many fighters have found refuge in the Kurdish enclave in Iraq since 1999, when the unilateral truce was declared.
Turkey has been frustrated by the reluctance of both Baghdad and Washington to take military action against the PKK in Iraq and Erdogan has spoken out about this in the past.