By Emre Peker

ISTANBUL—Turkey’s push to end a three-decade Kurdish insurgency got a significant boost from a call by the group’s jailed leader for his rebels to disarm if the government delivers democratic reforms.

The overture by Abdullah Ocalan on Saturday pushed stalled peace talks, now in their third year, into a crucial phase fraught with mutual mistrust. With just three months to parliamentary elections in June, Kurdish lawmakers pressing for a decentralized state are competing for votes with President Recep Tayyip Erdogan, who seeks to consolidate executive powers.

At stake isn’t only peace and security for Turkey, which has the world’s largest Kurdish population, but also the efficacy of the fight by an international coalition against the extremist group Islamic State.

Kurdish forces have proved to be the most effective ground force in the U.S.-led fight against the group, also known as ISIS. This has won the Kurds plaudits from the U.S. and Europeans and calls from Turkey’s allies in the North Atlantic Treaty Organization to remove Mr. Ocalan’s Kurdistan Workers’ Party, or PKK, from terrorist lists. Last month, French President François Hollande welcomed fighters from PKK’s Syrian affiliate to the Élysée Palace, showing how the Marxist group has evolved from pariah to military ally.

Despite decades of animosity, Turkey reluctantly offered rare cooperation with the PKK’s Syrian Kurdish allies in the battle for the Syrian city of Kobani on Turkey’s border in recent months. The government allowed Iraqi Kurdish fighters and weapons to transit through Turkish territory to Kobani—reinforcement that helped the Syrian Kurds push Islamic State from Kobani after months of ground battle backed by U.S.-led coalition airstrikes.

“The Kurds in Syria are the only bright spot in the fight against ISIS,” said Henri Barkey, a former State Department planner who now teaches international relations at Lehigh University.

“The majority of the PKK’s conflicts are currently in Syria, therefore it will difficult for it to lay down arms,” he said.

Kurds make up about 20% of Turkey’s 77 million population.

As a condition to end the military campaign by his PKK, Mr. Ocalan has demanded a new constitution that enshrines pluralistic democratic principles such as the recognition of ethnic identities and personal freedoms.

The rebel leader is also seeking to capitalize on the softening international stance against the PKK in his bid to set the domestic political agenda before June elections.

His olive branch sent tremors across Turkey’s polarized landscape over the weekend.

“This invitation is a historic declaration of an intention for armed struggle to be replaced by democratic politics,” Mr. Ocalan said Saturday in a statement. The Kurdish leader has been imprisoned in a Sea of Marmara island south of Istanbul since his 1999 capture.

He called on the PKK to convene an extraordinary meeting in the spring to take the necessary steps if the government delivers democratic reforms.

Signaling the difficult path to PKK’s disarmament, government officials and Kurdish decision makers immediately sought to shift responsibility, each tasking the other side with implementing steps to end the military conflict that Turkish officials say has killed 40,000 people.

“We hope that all parties will seize the opportunity to make decisive progress toward reconciliation and democratization,” said the European Union, which Turkey seeks to join. The bloc welcomed the PKK leader’s call to lay down arms as a “positive step forward.”

On Sunday, the PKK’s executive arm said the government bears the burden to meet Mr. Ocalan’s requirements.

With the government finally clinching a call for the PKK to disarm, Deputy Prime Minister Yalcin Akdogan urged Kurds on Saturday to implement concrete steps to end the military campaign.

While seconding the Kurdish call for a new national charter, the deputy premier didn’t commit to or comment on Mr. Ocalan’s demanded reforms, saying instead that there is “nothing that hasn’t been talked about.”

“On the one hand it seems to show that the government got what it wanted before the elections. On the other hand, it leaves room for Kurds to say their demands have not been met,” said Cengiz Candar, a columnist whose 2012 research on how the PKK would disarm serves as a reference for Turkey’s politicians. “The ambiguity is greater than the clarity.”

Meanwhile, nationalist lawmakers slammed the government for striking a deal they say amounts to treason, highlighting the political divisiveness of peace talks. Mr. Erdogan’s previous attempt to resolve the issue was derailed after secret meetings between PKK leaders and Turkish spies in Oslo were leaked in 2011. That year was the deadliest since the 1990s, with about 1,000 deaths.

A key indicator of the parties’ intentions will be the fate of a controversial domestic security bill, which would expand police powers to fire live rounds on protesters if attacked by Molotov cocktails, and detain people without judiciary approval.

The legislation followed violent demonstrations in October that left dozens dead in Turkey’s majority Kurdish southeast. They were protesting against the government’s perceived refusal to aid Syrian Kurds in the battle for Kobani.

While Mr. Erdogan has pledged to adopt the security measures that he argues are tantamount to Turkey’s stability and progress, opposition lawmakers including Kurds and the EU have slammed the bill for paving the way for human-rights violations.

“The security law isn’t legislation that will bring peace,” Kurdish lawmaker Selahattin Demirtas said after Saturday’s PKK disarmament announcement.

On Sunday, a Kurdish lawmaker Pervin Buldan said the law wouldn’t be adopted as is, adding that the government had “softened” its stance after Mr. Ocalan’s call.

The ruling Justice and Development Party dismissed links between the security measures and Kurdish peace-talks.

“We are always open to negotiations,” ruling party lawmaker Mahir Unsal said.

The Wall Street Journal