A senior figure in the Kurdistan Workers' Party (PKK) on Friday warned that Turkey would pay "a heavy price" for its offensive against the rebels amid new deadly clashes in the Kurdish-majority southeast.

A 40-year-old man was killed when he was caught in an armed clash between Turkish forces and the PKK in the city of Diyarbakir, security sources told AFP.

A 29-year-old man was also wounded during clashes that erupted overnight after youths linked to the outlawed PKK opened fire at police trying to clear a main road blocked by the militants.

After a series of attacks in Turkey, Ankara has launched a two-pronged offensive to bomb Islamic State (IS) militants in Syria and PKK rebels in northern Iraq and southeast Turkey.

So far, the operation has focused largely on the Kurdish rebels, who have responded by waging a bloody campaign against the security forces.

"We are waging a battle of the wills," the PKK's northern Iraq-based leader Murat Karayilan was quoted by the pro-PKK Firat news agency as telling Kurdish Sterk TV.

"We are experienced and we know very well what to do. They made a very big mistake by attacking us... They will pay a very heavy price for that."

According to an AFP toll, 31 members of the Turkish security forces have since died in attacks blamed on the PKK.

- 'They are doomed to fail' -

But Karayilan, who is often seen as the movement's overall leader in the absence its jailed iconic chief Abdullah Ocalan, said the PKK had not "put into effect a war plan yet."

"Our fight continues in a planned and controlled way. We are just conducting retaliatory actions," he said.

The PKK has waged an over 30 year struggle for autonomy and greater rights in Turkey's Kurdish majority southeast that has claimed tens of thousands of lives.

Meanwhile, more than 2,000 people took to the streets in Diyarbakir on Friday to protest the escalating cycle of violence that has left a 2013 ceasefire agreed by the PKK in tatters, an AFP reporter said.

Turkish President Recep Tayyip Erdogan on Friday vowed that his government would press on with its relentless campaign against Kurdish militants, saying the operations were not "temporary."

"You shall not think they are strong... They are doomed to fail," Erdogan told supporters in his ancestral hometown in the Black Sea province of Rize.

More than 1,700 suspects have been arrested since late last month in police raids nationwide targeting suspected members of the PKK as well as IS and the Marxist Revolutionary People's Liberation Party Front (DHKP-C), state-run Anatolia news agency said.

On Friday, police detained at least 39 suspected terrorists in raids in several cities including Istanbul, Ankara and Izmir, Anatolia said.

Karayilan meanwhile distanced the PKK from the killing on July 22 of two Turkish policeman in their sleep as one carried out "by a group not precisely affiliated to us".

He also said the PKK's central command did not approve of suicide bombings, such as an attack in Istanbul on Monday that was claimed by Kurdish militants.