Murat Karayilan, the group's second in command, told the AFP news agency: "We are ready for a ceasefire on September 21 coinciding with World Peace Day. Turkey should be ready to respond and flexible in this regard."
The offer has come in response to recent pressure from the US on the the Kurdish issue in Iraq, according to Turkish media figures.
Yusuf Kanli, editor-in-chief of the Turkish Daily News, told Aljazeera: "The moment the US state department issued a call to the gang to lay down arms, we knew that at some stage the PKK would make a statement, offer a conditional or unconditional ceasefire and demand from the Turkish state to accept it as an interlocutor."
The call by the US for the PKK to lay down its arms was issued on August 15, the day that marked the 23rd anniversary of the start of PKK attacks in Turkey's southeast.
Nuri al-Maliki, the Iraqi prime minister, has assured Turkish leaders that his country will not be a sanctuary for the PKK.
Maliki told Recep Tayyip Erdogan, the Turkish prime minister, by telephone this week: "We will not allow Iraq to serve as a base for the PKK."
"What’s certain is the bitter reality that it will be very difficult for any government in Ankara to send and maintain Turkish troops in southern Lebanon if PKK violence continues"
Yusuf Kanli, chief editor at the Turkish Daily News
Turkey said only last month that it was prepared to send troops to the Iraqi border to intervene in military operations to crush the PKK bases in northern Iraq if Baghdad and Washington failed to take any action.
The Turkish government is having second thoughts about sending troops to Lebanon, now that the US has suggested that an international force should disarm Hezbollah, Turkish diplomats said on Wednesday.
Kanli believes that this is tied into the PKK issue: "What’s
certain is the bitter reality that it will be very difficult for any government in Ankara to send and maintain Turkish troops in southern Lebanon if PKK violence continues and Washington maintains its policy of keeping northern Iraq off limits for the Turkish military."
"Especially when, meanwhile, the US military ... remain inactive against the PKK hideouts in the Kandil Mountains, some 90 kilometres away from the Turkish border."
Kanli told Aljzeera that public opinion would not support such a move and that casualties that could arise from such a mission in Lebanon would hurt the reputation of the Turkish military when it comes to tackling the PKK.
"We don't need casualties at a time when we are fighting our own war," he said.
The PKK is considered a terrorist organisation by the US, the EU and Turkey, making any type of diplomatic solution with group a sensitive one for Ankara.
Tensions in the south east of
Turkey have been on the rise
Kanli said that Ankara will not publicly enter into discussions with the PKK and will reject all conditions, but that behind closed doors discussions could take place.
"We have sufficient information accumulated from the ’90s, as well as from the testimony of the separatist chief Abdullah Ocalan during his trial, that there have indeed been times when the Turkish state or some top Turkish officials exchanged messages.
"However, like the US and many other countries, 'no talk to terrorists' is the established state policy of this country. Exceptions are for exceptional times. Even if the PKK's offer won't be taken seriously, the ball is in the government's court."