The jailed Kurdish guerrillas' leader, Abdullah Öcalan , has used the Kurdish new year celebrations to call a ceasefire in the 30-year war with the Turkish state in the biggest boost to an incipient peace process in years.

"The weapons should fall silent, politics should speak," said a statement on Thursday from Öcalan broadcast on Kurdish TV, as hundreds of thousands of Kurds thronged the streets of the south-eastern city of Diyarbakir, their capital, for the Newroz new year celebrations.

The statement from the PKK leader, who has been held in solitary confinement in an island prison south of Istanbul for 14 years, was the strongest signal to date that peace talks launched tentatively last October with the government of Recep Tayyip Erdoğan are building momentum.

The Öcalan statement added that the estimated 3,500 PKK fighters inside Turkey should leave the country for their strongholds in the Qandil mountains of northern Iraq. "This is not the end. This is the beginning of a period," said the declaration.

In an important symbolic gesture last week, the PKK released eight Turkish hostages who had been held captive in northern Iraq for up to two years. But in a sign of the possible backlash to come, a leftist group scornful of the rapprochement launched a bomb and missile attack on government buildings on Wednesday night. One person was injured.

"The announcement of the ceasefire will be one of the most important steps ever in the history of this conflict," Mesut Yeğen, a historian of the Kurdish issue, said. The ceasefire will be the first step of a so-called roadmap proposed by Öcalan a couple of weeks ago.

If successful, it would further reinforce peace talks that began in October last year and that might yet spell the end to the devastating conflict that has claimed more than 40,000 lives since it erupted in 1984.

In further steps, PKK fighters are expected to withdraw from Turkish territory to northern Iraq, where the PKK, labelled a terrorist organisation by both the US and the European Union, maintains bases. A third step would include the disarmament and reintegration of PKK guerrillas.

Sadullah Ergin, the Turkish justice minister, told reporters on Monday that he expected all three steps to be successfully completed by the end of 2013. If the PKK heed their leader's call, the entire organisation's estimated 3,500 fighters based in Turkey will have withdrawn by August.

While Öcalan stressed in his peace roadmap that the Kurds did not demand a separate independent state, he did underline the importance of substantial constitutional and judicial changes that would guarantee Turkey's Kurdish population all cultural rights and give more power to local authorities.

Yeğen said: "The fact that the PKK does not want to withdraw all of its fighters before the announcement of the new constitution also means that they want to keep an ace up their sleeve during the negotiations of constitutional changes. But the government seems to have accepted this condition."

There have been attempts at peace negotiations before, but this is the first time that a Turkish prime minister and Öcalan, deemed the conflict's chief villain by many Turks, are openly engaging in dialogue.

Cengiz Aktar, a columnist, warned that a successful completion of the three steps of the peace negotiations would not mean an immediate solution of Turkey's Kurdish problem. "We would enter a post-conflict era, but this era will last a long time," he said. "There are no quick fixes in conflict resolution."