Turkish Prime Minister Ahmet Davutoglu on Sunday vowed that peace with Kurds would be achieved, seeking support from the country's largest minority group in a key visit to the southeast.

"The peace process will definitely reach success in any case and eternal brotherhood... will prevail," Davutoglu told a cheering crowd in the Kurdish majority city of Diyarbakir.

"We will walk altogether in the streets of Diyarbakir. We will walk shoulder to shoulder anywhere in the world, let it be Diyarbakir or the Middle East, as equal members of our nation," he said.

Turkey's peace process with the outlawed Kurdistan Workers' Party (PKK) appeared to be making progress until a standoff over the key Syrian Kurdish town of Kobane late last year.

Over 30 people were killed in October when Kurdish anger over Turkey's strategy against the Islamic State (IS) insurgency spilled onto the streets.

The PKK, whose rebellion for self-rule left 40,000 dead, has warned that a fragile ceasefire that has largely held since 2013 will be over if Kobane falls to jihadists.

Davutoglu on Sunday lauded the peace process as a "project of brotherhood" between Turks and Kurds, not a "conjectural" manoeuvre to win elections.

The prime minister saluted Kurds in their own language, drawing bursts of applause, saying: "I want to learn our nice Kurdish language if I can find some time."