The Kurdish Communities Union, the urban unit of the blacklisted group known by the initials PKK, also said in a statement it would honor a cease-fire with Turkish forces, the Hurriyet Daily News reported Monday.
Turkish Prime Minister Tayyip Erdogan, who has a political stake in the peace process, reportedly said last month the PKK, listed as a terrorist organization internationally, hasn't upheld its end of the agreement, with only 20 percent of militants leaving Turkey, mostly women and children.
A senior PKK leader, Cemil Bayik, had told the BBC that the militant group would "continue to make efforts until Sept. 1."
Bayik said in that earlier interview that imprisoned PKK leader Abdullah Ocalan Aop also is working to maintain the peace.
"If they [government officials] do not take necessary steps for the second phase of the process, there will be nothing we can do," Bayik said in the BBC interview. "If we cannot see this, we will stop withdrawing ... ."
To keep the peace process moving ahead, the government had been expected last month to start debating a reform package meant to bolster Kurdish rights and enhance democracy, Hurriyet said.
The newspaper did not report the status of the reform package.
Erdogan, who has been criticized for offering concessions to the militants, has said the measures would not "disturb the Turkish public."