Kurdish rebel fighters have stopped withdrawing from Turkish soil, citing failures by the government to take steps agreed under a peace process, but have vowed to maintain a ceasefire for now, Reuters news agency has reported quoting local website Firat News.

Kurdistan Workers Party (PKK) fighters started withdrawing in May but the push to end a conflict that has cost more than 40,000 lives has become increasingly frayed, with both sides accusing each other of failing to keep their side of the peace deal.

PKK leader Abdullah Ocalan, jailed on an island near Istanbul, declared a ceasefire in March after months of talks with the Turkish state and his fighters began moving to Iraq two months later under a deal envisaging increased rights for Kurds.

"While the withdrawal is halted, the ceasefire position will be maintained so as to give (the ruling) AK Party an opportunity to take steps in line with Leader Apo (Abdullah Ocalan)'s project," the KCK - the rebels' umbrella political group - said in a statement on Monday.

The Turkish Prime Minister Tayyip Erdogan, who has staked much political capital in the peace process, was quoted last month as saying the PKK had not kept its promise, with only 20 percent of rebels leaving Turkey, mostly women and children.

Turkey, the United States and the European Union all call the PKK a terrorist organisation. It took up arms to carve out an independent homeland in the southeast but later scaled back its demands to greater cultural rights and autonomy.

The conflict, stretching back over three decades, has stunted the development of one of Turkey's poorest regions and prompted tens of billions of dollars of military spending that have weighed on the state coffers.

The ceasefire has largely held but PKK commanders had warned of new clashes if Turkey did not take concrete steps to advance the process by September.

In addition to more Kurdish-language education, the Kurds, who dominate Turkey's southeast and account for about a fifth of the population, want anti-terrorism laws softened, the electoral threshold to enter parliament lowered from 10 percent, and more powers for local governments.