This week, one of Turkey’s most powerful politicians made a surprising offer to the militant leader he has long branded a “baby killer” and “chief terrorist.”

If Abdullah Ocalan, the leader of the main group fighting for greater autonomy for Turkey’s Kurdish minority, would come to Parliament, renounce militancy and disband his organization, the politician said, it could open a pathway to end his life sentence in a Turkish prison.

The offer by the politician, Devlet Bahceli, fell far short of a breakthrough in efforts to end decades of bloody conflict between the Turkish state and Mr. Ocalan’s group, the Kurdistan Workers’ Party, or P.K.K. But it was one of several recent gestures suggesting a new openness in the Turkish government to the possibility of revived peace talks.

Then on Wednesday, the government blamed the P.K.K. for a deadly attack on a state-run aerospace company. The attack did not appear to derail the positive momentum.

Turkey has been trying to stamp out the P.K.K. since its founding as an underground militant organization in 1984. Tens of thousands of people have been killed in the years since in P.K.K. guerrilla attacks and the Turkish military’s responses. Turkey and its Western allies consider the P.K.K. a terrorist organization.

Turkish authorities captured Mr. Ocalan in 1999 and sentenced him to life in prison, locking him up on an island in the Sea of Marmara where he was for many years the only prisoner. The government started peace talks with the P.K.K. in 2012, but negotiations collapsed in 2015, unleashing a new wave of violence that washed away any hopes for a truce.