"We will resolve all problems with more democracy, more civil rights and more prosperity," he said, frequently interrupted by applause from a crowd of some 1,000 people.
In Arbil, northern Iraq, a senior Turkish Kurd rebel leader welcomed Erdogan's statement, but said he wanted to see how this translates into action.
"We believe Erdogan's statements are significant," but what matters is what concrete actions will be taken on the ground, Zubeyir Aydar, head of KONGRA-GEL, a sub-group of the rebel Kurdistan Workers' Party (PKK), said in a statement received by AFP.
Erdogan was seeking to allay concerns that a recent increase in attacks on military and civilian targets blamed on the PKK might prompt Ankara to introduce measures that would diminish the fragile freedoms the sizeable Kurdish minority has only recently gained.
Keen to boost its bid to join the European Union, Ankara has ended 15 years of emergency rule in the southeast and allowed the Kurdish language to be taught at private courses and used in public television and radio broadcasts.
The Kurdish conflict has claimed some 37,000 lives since 1984, when the PKK took up arms for Kurdish self-rule in the southeast, ravaging the meager infrastructure and the mainstays of farming in the region and forcing poor peasants to migrate en masse into urban slum areas.
The brutal state response to PKK violence also led to gross human rights breaches on both sides and opened a wide confidence gap between Ankara and the Kurds, who make up about a fifth of the country's 70-million population.
The PKK, blacklisted as a terrorist group by Turkey, as well as the United States and the EU, has markedly stepped up violence over the past few months after calling off a five-year unilateral truce in June 2004 that had brought relative peace to the turbulent southeast.
Erdogan's visit in Diyarbakir took place under tight security, with some 3,000 security forces on duty across the city.
Scores of policemen lined up on the road leading from the airport to the city center and snipers were seen positioned on rooftops along the prime minister's route.
Erdogan signalled that Ankara would not back down from military measures in the struggle against the PKK.
"Terrorism and violence are the worst enemy of this country and they will never be tolerated," he said, vowing an "all-out unshakeable determination" to counter violence.
Many Kurds complain that the government has not done enough to relieve their chronic poverty, but Erdogan made it clear that Ankara planned no industrial investments in the region, calling on local businessmen to take the initiative under a recently introduced scheme of incentives.
Diyarbakir Mayor Osman Baydemir, a leading Kurdish politician, welcomed Erdogan's promise for a democratic settlement of the Kurdish question.
"I hope his pledges will lead to the opening of a new page" in Ankara's ties with the Kurds, Baydemir told NTV television.
"A new ground is required to ensure that the arms are silenced. My hopes in this direction were boosted today," he said.
In his statement, Aydar said, "we also believe that a new page should be opened," but he noted that Erdogan failed to say whether the government was considering an end to military operations against the PKK.
"He said nothing on issues that are important to us," Aydar said, alluding also to the solitary confinement of jailed PKK leader Abdullah Ocalan on a prison island in northwestern Turkey.
The PKK, as well as many mainstream Kurdish politicians, have called for a general amnesty for PKK rebels that will ensure their participation in political life.
They also demand that the Kurdish language be taught in public schools, that laws restricting Kurdish representation in parliament be repealed and that Kurdish localities given Turkish names revert to their former appelations.