Kurdish rebels have demanded that the Turkish government take steps to advance the fragile peace process by September or face unspecified action, a pro-Kurdish news agency reported on Wednesday.

"A step must be taken. September 1 is the deadline," Cemil Bayik, the new hawkish leader of the Kurdistan Workers' Party (PKK), was quoted as saying by Firat news agency.

"If no step is taken before September 1, it will be understood that the aim is not a solution," he said, warning that Kurdish people would then have to defend themselves, without elaborating.

His comments came after the PKK earlier this month issued a "final warning" to the government, accusing it of sabotaging the peace process designed to end nearly three decades of insurgency.

The PKK had criticised the government of Prime Minister Recep Tayyip Erdogan for building new army barracks in majority-Kurdish areas, while allowing Kurdish militias to continue operating on behalf of the regular army.

Jailed PKK leader Abdullah Ocalan has been in negotiations since late 2012 with Turkish authorities for an end to the Kurdish conflict, which has cost some 45,000 lives since 1984.

Ocalan, serving a life sentence for treason and separatism on Imrali island off Istanbul since 1999, announced a historic ceasefire with the government in March.

As part of the truce, the PKK -- listed as a terrorist organisation by Ankara and its Western allies -- agreed to withdraw its estimated 2,000 fighters from Turkey to their bases in northern Iraq.

In return, it is seeking wider constitutional rights for Turkey's 15 million Kurds.

But the peace process has been rattled by the death of a young Kurdish man during an anti-government protest in the Kurdish majority southeast last month.