The outlawed Kurdistan Workers Party's 30-year conflict with Turkey is coming to an end, the group's jailed leader said on Saturday, hailing the start of a new democratic process in the country.

The PKK, which for three decades fought a bloody insurgency for self-rule for Turkey's Kurdish minority that cost 40,000 lives, launched its armed struggle on August 15, 1984.

But the group's jailed leader Abdullah Ocalan said in a statement from his cell on the prison island of Imrali in the Sea of Marmara that Turkey was now on the verge of "historic developments" after last week's presidential elections.

"On the occasion of the 30th anniversary of our struggle, I want to state that we are on the verge of historic developments," Ocalan said in a statement quoted by the Firat news agency, which is close to the PKK.

"This 30-year war is -- through a major democratic negotiation -- at the stage of coming to an end."

"The process of democratic negotiations has a profound meaning, historically and socially," he added.

He said that the process could become a model for solving conflicts not only in Turkey "but in the entire region".

- 'No longer a utopia' -

Ocalan's statement follows a meeting on Friday on Imrali between him and representatives of the pro-Kurdish People's Democratic Party (HDP).

The presidential election was won by Prime Minister Recep Tayyip Erdogan, but the HDP's candidate Selahattin Demirtas polled a respectable 9.8 percent in what Ocalan said was a breakthrough for Turkish democracy.

He said that the HDP was capable of becoming the main opposition to Erdogan, and even one day replacing his ruling AK party in government.

"With these results, the HDP, with its broadest base will be today's democratic opposition and the future's democratic ruling party," Ocalan said.

The election had opened the way to clear "extreme nationalist and fascist policies" from Turkey, he said.

Ocalan said that the new period of transition was about "moving the idea of a democratic Turkey from a utopia to a reality".

During the presidential election campaign, Demirtas tried to expand the appeal of the HDP to encompass not just Kurds but secular Turks attracted by its socialist, pro-women and pro-gay message.

Erdogan has also sought to ease tensions with the Kurdish minority by implementing reforms, notably on the use of the Kurdish language.

His government launched clandestine peace talks with Ocalan in 2012 but the talks stalled in September when the rebels accused the government of failing to deliver on reform.

Parliament last month adopted a new reform bill aimed at kick-starting the talks, which was hailed by Ocalan.

The moves come as PKK rebels and other Kurdish fighters play a lead role in combatting the advance of Islamic State (IS) militants in northern Iraq.

In his message from prison, Ocalan hailed the fighters from the PKK, Iraqi Kurdish peshmerga and other Kurdish fighting units who have joined forces against the IS, saying they were "resisting for the sake of our freedom".

The PKK is still classified as a terrorist group not just by Turkey but also the United States and the European Union, complicating its role in the US-backed Kurdish actions against IS.

The PKK's military leader Murat Karayilan, who heads the armed PKK rebels at their Kandil Mountain base in northern Iraq, called this month for a "national resistance front" between Kurdish groups to combat the jihadists.