Pervin Buldan and Mithat Sancar of the Peoples' Equality and Democracy (Dem) Party were meeting the Turkish leader at his presidential complex in the capital Ankara, the party said in a statement. The talks were still under way on Thursday evening.

Dem has been mediating between the Turkish government and the PKK, which has waged a four-decade insurgency against the state.

The group, which says it has used armed struggle to secure better rights for Turkey’s Kurdish ethnic minority, is listed as a terrorist organisation by Ankara, the EU and the US.

Ms Buldan and Mr Sancar are part of a delegation that has been allowed relatively frequent visits to the PKK’s jailed leader Abdullah Ocalan since the group's dissolution process began. Their mediation between Ocalan and Turkey’s leadership is the closest that the two sides have come publicly in decades.

On Sunday, the PKK announced it was withdrawing from Turkey and sending its fighters to its mountain bases in Iraq’s Kurdistan region.

In February, Ocalan, who is serving a life sentence in a remote island prison near Istanbul, called on members to disarm and dissolve the group that he founded in the late 1970s. In July, PKK fighters burnt some of their weapons in what Kurdish politicians in Turkey described as a sign of the militants' readiness to move away from armed struggle.

The group's dissolution would end one of the Middle East’s longest conflicts, which has defined modern Turkey and caused the deaths of at least 40,000 people on both sides.

Kurdish politicians and PKK members expect the Turkish government to lay out concrete paths for former fighters to reintegrate into society. Parliament has formed a 51-member commission to propose legal changes to allow amnesties for former fighters, the release of prisoners jailed on PKK-related charges and wider cultural rights for Kurds in Turkey.

Dem party officials are calling for an acceleration in what they describe as process for “peace and a democratic society”. Turkish government officials frame the process as one leading to a “terror-free Turkey”.

But amnesties, prisoner releases and wider rights for Turkey’s Kurds face opposition from other stakeholders in the country. Some political parties and groups representing Turkish army veterans oppose what they see as concessions to the PKK forming any part of the dissolution process.

The commission has not yet announced any firm steps forward, although parliamentary speaker Numan Kurtulmus said on Thursday that it would present the wider parliament with “a framework to determine next steps” to be taken once Turkish authorities are convinced that the PKK has dissolved itself.

“We hope that the organisation … will also eliminate its presence beyond our borders as soon as possible and that we will enter a period where terrorism is no longer mentioned not only in Turkey but also in Syria, Iraq, Iran and other regions,” Mr Kurtulmus said in a speech after the PKK’s announcement that it was withdrawing from Turkey.

Over decades, the PKK’s presence has extended beyond Turkey, and the group’s affiliates control swathes of territory in neighbouring Syria, as well as bases in Iraq and Iran.

Dem party co-chair Tuncer Bakirhan said the dissolution process “must evolve through laws, rights and freedoms”.

“The Parliament must facilitate this process and make the necessary legal arrangements for the transition period,” he told a press conference in Ankara.

He also called for “free working conditions, communication, and living conditions” for Ocalan to enable him to play “a more active role” in the road to peace, he added.

Ocalan has been in jail since 1999, after being captured by Turkish commandos in Nairobi. His death sentence for treason, separatism and leading an armed terrorist organisation was commuted to life imprisonment in 2002, when Turkey abolished capital punishment.

Thursday's meeting os third between Dem party officials and Mr Erdogan since the start of the PKK’s dissolution process. The first meeting in April prompted pro-Kurdish politicians to express greater hope over the prospects of a new era of Kurdish-Turkish relations. The two sides met again in July.