Security sources said one protester died in Saturday's clashes and 10 people were injured.
The latest clashes erupted near the Syrian border in Kiziltepe, a town of around 100,000 people south of the mainly Kurdish region's largest city Diyarbakir, where most of this week's violence was focused.
About 1,000 demonstrators set fire to the branches of at least two major banks and a building used by the ruling Justice and Development Party (AKP).
Youths set up barricades with rubbish bins and rocks on one street corner as armoured vehicles patrolled up and down the road. A mechanical digger cleared debris from the main street.
At one traffic circle army marksmen crouched with rifles and observed the youths from a distance.
Police and protesters also clashed in the town of Silopi, near the Iraqi border, on Saturday. Demonstrators threw stones and sticks at the police who responded by firing tear gas.
A three-year-old boy died of gunshot wounds on Friday in Diyarbakir and local media said he was killed after police fired shots over the heads of protesters.
Three children have died since the clashes erupted earlier this week."The state is deliberately raising tensions and provoking the people. We will respond in kind," one man, Davut, 36, said.
Several protesters threw stones at a Reuters cameraman trying to film the demonstration.
"We are very sad about what happened to this man in the prime of his life," Cihan Sincar, the mayor of Kiziltepe, told Reuters when asked about the death.
"Our wish is that this trouble should come to an end," she said, adding that Ahmet Arac, who was about 24 years old, was shot in the head during protests in the town centre in the morning. It was unclear who shot him, she said.
Seven people have been killed in
the southeast in recent days
The latest death brought the toll in this week's violence - Turkey's worst civil unrest in decades - to eight dead.
Riots erupted on Tuesday after funeral ceremonies for 14 members of the outlawed Kurdistan Workers Party (PKK) killed last weekend by security forces.
Tayyip Erdogan, Turkey's prime minister, said late on Friday children were being used as "pawns of terrorism" in unrest gripping the Turkey's southeast and warned that security forces could not guarantee their safety.
He accused those behind the riots of trying to split the country, saying: "We shall never allow anyone to perform surgery on the unitary structure of our country".
Diyarbakir, a city of around one million people, was calm on Saturday and shopkeepers opened their stores after keeping them shut at the height of the trouble.
Security sources said 198 people, including 31 children, had been remanded in custody in Diyarbakir since the riots began.
Ankara has lifted restrictions on the Kurdish language and culture in EU-linked reforms over the past few years, but critics say it needs to do much more.
The EU, which Turkey aims to join, has expressed concern about the violence and urged Ankara to do more to combat poverty in the southeast and to boost Kurds' cultural rights.