The outlawed Kurdistan Workers Party (PKK) militia declared an immediate ceasefire on Saturday, a news agency affiliated with the group said, heeding jailed leader Abdullah Ocalan’s call for disarmament, in a major step toward ending a 40-year insurgency against the Turkish state.

Ocalan on Thursday called on the PKK to lay down its arms and dissolve, a move that President Tayyip Erdogan’s government and the opposition pro-Kurdish DEM party have voiced support for.

If successful, the move could have wide-ranging implications for the region, while ending a conflict that has killed more than 40,000 people since the PKK - now based in the mountains of northern Iraq - launched its armed insurgency in 1984.

The group said in a statement it hoped Ankara would release Ocalan, held in near total isolation since 1999, so he can lead a process of disarmament, adding that the necessary political and democratic conditions need to be established for the process to succeed.

“We, as the PKK, fully agree with the content of the call and state that, from our front, we will heed the necessities of the call and implement it,” the group said, according to the Firat news agency.

“Beyond this, issues like laying down arms being put into practice can only be realised under the practical leadership of Leader Apo,” the group said, using its nickname for Ocalan, adding it would halt all hostilities immediately unless attacked.

The DEM party urged the government on Friday to take steps towards democratisation, saying its response was critical. The government has said it would not negotiate with the PKK and that all Kurdish militias, including in Iraq and Syria, must lay down their weapons.

While welcoming Ocalan’s appeal as positive, the U.S.-allied Syrian Democratic Forces (SDF), which Ankara deems an extension of the PKK, has said it did not apply to them.

Ankara has repeatedly called on the SDF’s armed wing to disarm since the fall of Syrian President Bashar al-Assad last year, warning that it would face military action otherwise.

Ocalan’s call, prompted by a surprise proposal in October from an ultra-nationalist ally of Erdogan, has been welcomed by the United States, the European Union and other Western allies, as well as by Turkey’s neighbours Iraq and Iran.