The fresh fighting erupted during funerals for two young men and an eight-year-old boy killed during Wednesday's clashes in Diyarbakir, the main city of Turkey's mainly Kurdish southeast.
The boy and one man were shot dead. The other man was crushed under a police armoured car, witnesses said. An investigation into the deaths has begun, the governor said.
Some mourners, ignoring appeals for calm from local officials, attacked a police station. Police fired warning shots into the air with AK-47 assault rifles and sprayed tear gas.
A masked man in his 20s, said: "We are angry about the three people killed yesterday, that's why we are here."
The nearby town of Batman also saw street battles between riot police and up to 3,000 protesters on Thursday. CNN Turk television said 10 people had been hurt in those clashes.
Police have detained at least 200 people in Diyarbakir since the violence began on Tuesday during funeral ceremonies for 14 fighters of the banned Kurdistan Workers Party (PKK), killed by security forces last weekend.
In Diyarbakir, a city of nearly one million, most shops and offices remained shut on Thursday and roads were blocked by barricades of burning tyres. The army deployed armoured vehicles in suburbs to discourage protesters.
Police have killed three in the
Paramilitary police protected key buildings, including the governor's office. Protesters have targeted banks, shopping centres and offices of Turkey's ruling Justice and Development Party (AKP).
Tayyip Erdogan, the Turkish prime minister, said the government and security forces had the situation under control.
"Our people should feel at peace, they will be safe. Security forces will do what is necessary," he told a news conference.
In a sign of increasing political tension, Turkey's Interior Ministry said it was investigating comments by Osman Baydemir, Diyarbakir's mayor, for expressing sympathy with the protesters.
Ankara suspects Baydemir, whose Democratic Society Party seeks more cultural and political rights for Turkey's estimated 12 million Kurds, of having links to the banned PKK.
"Using children and women for a terror struggle is a disrespect to humans ... . It is out of question that the government will tolerate any action outside the law. Nobody should expect us to bargain," Erdogan said.
Political analysts say this week's riots are rooted in high unemployment, poverty and a belief among the Kurds of the region that Ankara is not seriously interested in improving their lot.
"We are angry about the three people killed yesterday, that's why we are here"
Under pressure from the European Union, which it hopes to join, Turkey has removed some restrictions on Kurdish language and culture, but critics say it is too little too late.
Ankara holds the PKK responsible for the deaths of more than 30,000 people since it launched its armed campaign for an independent Kurdish state in southeast Turkey in 1984.
Most of the dead were PKK fighters killed by the armed forces.
The PKK blamed Turkey for ignoring its peace overtures and called for more demonstrations.
"We are calling on ... the Kurdish people to carry on indefinitely their struggle through legitimate democratic action until a democratic solution is brought about," the PKK said in a statement on a website it uses.
The government is also under fire from Turkish nationalists who view the concessions to Kurds as rewarding terrorism.
Erdogan infuriated nationalists last summer when he visited Diyarbakir and said Turkey had made mistakes in the past in its handling of what he called the "Kurdish problem".
The PKK is also on the terrorism blacklist of the European Union and the US.