Turkey`s chief of staff said in a statement that grenades thrown by the militants ignited a fire in the heavily forested area where the clash occurred and 13 soldiers died in the blaze.
It said seven soldiers were wounded.
The pro-Kurdish Firat news agency disputed the official version with a report that quoted a witness saying a Turkish warplane had targeted the militants in an air strike which also killed the soldiers positioned nearby. It gave no death toll.
Prime Minister Tayyip Erdogan met the army and intelligence chiefs as well as the interior minister and head of the paramilitary gendarmerie in Ankara.
"Turkey will succeed in overcoming the terror and the powers behind it without compromising democracy, justice and brotherhood," Erdogan said in a statement.
Security forces, backed by warplanes, launched a hunt for the rebel fighters in the mountains of Diyarbakir province, and the military chief of land forces had gone to the area.
The PKK moved to what it calls an "active defence" stance, whereby its fighters defend themselves if threatened, after ending its 6-month-old ceasefire.
Last week the jailed leader of the PKK, Abdullah Ocalan, sent word through his lawyers that he had agreed with Turkish officials to set up a "peace council" aimed at ending the 27-year separatist conflict.
Ocalan said the council should be formed within one month, though it was unclear what form it would take.
The proposal came a month after Erdogan`s AK Party won an election for a third term in power and two months after Ocalan threatened "war" unless the government entered talks.
Boycott
Deputies from a pro-Kurdish party regarded as close to the PKK failed to reach a deal with the AK Party on ending their boycott of parliament, representatives of the two sides told reporters after a second day of talks on Thursday.
The boycott by the Peace and Democracy Party (BDP) deputies was prompted by court rulings barring some of its jailed elected candidates from taking their seats.
Reacting to news of the clash, BDP leader Selahattin Demirtas said: "We are really sad. Those friends are paying the price for the stalemate in politics. The Turkish parliament should take the initiative to bring peace."
And in Diyarbakir on Thursday, the Democratic People`s Congress, which bands together Kurdish non-government organisations, met and declared "democratic autonomy", though it was unclear what action that might entail.
Erdogan`s government won a confidence vote on Wednesday to push ahead with plans to rewrite the constitution, but the Kurdish boycott remains a hurdle to replacing the constitution created after a 1980 military coup.
More than 40,000 people have been killed in the conflict, though violence faded after Ocalan was captured in 1999.
Regardless of the "active defence" stance there has been a steady stream of militant activity in recent weeks.
PKK rebels abducted two people after stopping their vehicle in mountainous Tunceli province in eastern Turkey on Wednesday night, security sources said. They were labourers working on a military building, TV reports said.
A few days earlier the militants abducted three people, two of them soldiers, in Diyarbakir in the mainly Kurdish southeast.
Security forces were conducting a major operation to find them.
Separately, security sources said 14 PKK members surrendered to Turkish forces in Silopi, near the border with northern Iraq on Wednesday, allegedly due to maltreatment in militant camps.
There was no statement on the incidents from the PKK. (*)
Editor: Kunto Wibisono
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