"Our security forces are strong... and I believe they will make them pay a heavy price," Prime Minister Recep Tayyip Erdogan told reporters after Thursday's bloodshed, which sparked outrage across the country.
The army said 13 soldiers had been killed in "a fire sparked by the impact of hand grenades" hurled by militants of the outlawed Kurdistan Workers' Party (PKK) during close combat in forests in Diyarbakir province.
Seven PKK rebels were killed in the clashes, which left another seven soldiers injured, it said.
Erdogan lashed out also at the Kurdish Peace and Democracy Party (BDP), which is close to the PKK, saying it should not expect Ankara to bow down to violence and make concessions in faltering efforts to end the 26-year conflict.
"I'm openly telling the terrorist organisation and its extentions that they should never expect any good will on our part in the face of such ill-intentioned actions," Erdogan said.
"If they want peace, there is one thing to do: the terrorist organisation must lay down arms," he said, referring to the PKK.
"If they refuse to lay down arms, neither military operations will stop nor the (reconciliation) process will advance," he added.
There was more bloodshed in the southeast late Friday as a police car came under fire while patrolling the streets in the city of Siirt, Anatolia news agency reported.
A police officer died of his wounds in hospital, it said, adding that the security forces had launched an operation to hunt down the assailants.
Erdogan dismissed a declaration of "democratic autonomy" for the southeast made Thursday by a Kurdish umbrella organisation as a "self-styled thesis".
Prosecutors Friday launched an investigation into the declaration, Anatolia said. The mounting violence added to tensions between Ankara and the Kurds that have been on the rise since June 12 general elections.
Thirty Kurdish-backed lawmakers have boycotted the new parliament after the authorities refused to release six Kurdish activists elected while awaiting trial in prison, and stripped one of them of his parliamentary seat.
Ankara has held sporadic contacts with jailed PKK leader Abdullah Ocalan, who retains his influence over the Kurds, in a bid to reach a peaceful end to the conflict.
The effort however has faltered amid continuing violence and a nationalist backlash in a country where many see the PKK as a public enemy number one.
They hold it responsible for the some 45,000 deaths the conflict has caused on both sides.
Kurdish nationalists demand constitutional recognition for the Kurds, regional self-governance and Kurdish-language education in schools.
Many other Kurds however support Erdogan's Islamist-rooted Justice and Development Party, which put up a strong performance in the southeast in the elections.
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