The European Parliament's Foreign Affairs Committee passed a resolution Thursday saying "renewed mutual engagement" is needed to maintain a constructive relationship with Turkey.
Turkey's geopolitical rows with Cyprus, the Kurdish issue and judicial reform have presented obstacles to its move to establish a closer relationship with the European Union.
The Kurdistan Workers' Party, known by its Kurdish initials PKK, has been fighting the Turkish government since the 1980s.
Cyprus has been divided into a Republic of Cyprus and the Turkish-occupied north since 1974. Turkey doesn't recognize the Republic of Cyprus, a member of the European Union.
"Members of Parliament welcome direct political dialogue between the Turkish government and former PKK leader Abdullah Ocalan," a European statement read. "This might open up the prospect of an historic agreement settling the Kurdish conflict in a peaceful and democratic way."
Ocalan said in a letter Thursday he was ready to end an armed struggle against the Turkish government.
Turkish Prime Minister Recep Tayyip Erdogan said he welcomed the efforts at peace.
"We would like to see the reflections of Ocalan's remarks in the shortest period of time," he was quoted by Turkish newspaper Hurriyet as saying. "Once this comes to practice, the atmosphere in Turkey and the region will change."