In Istanbul, three people were reported killed after a molotov cocktail was thrown at a bus on Sunday.
Security sources said additional troops were being deployed to Kiziltepe on Sunday, a town of about 100,000 people south of the region's main city of Diyarbakir.
In Ankara, parliament called a special session for Tuesday to discuss the violence.
The southeast has suffered its worst riots in many years since Tuesday's funeral of 14 armed separatists killed in clashes with the army. Tensions reflect discontent over local conditions and resurgence of a Kurdish guerrilla campaign.
Police said Mehmet Sidik Onder, 22, received a bullet wound to the stomach after police fired in the air to stop a march in Kiziltepe, near the Syrian border. The protesters were heading for the home of another man shot dead in the town on Saturday.
Witnesses said the police fired at the man, the ninth to die in a wave of unrest that could stir serious strains in Tayyip Erdogan, the prime minister's, ruling Justice and Development Party and stoke tensions with the influential military.
Events are watched closely by the European Union that Turkey seeks to join.
A molotov cocktail attack set ablaze a bus in Istanbul late on Sunday, resulting in three deaths, the CNN Turk news channel reported.
A group of protesters hurled a molotov cocktail onto a bus in Istanbul's Bagcilar suburb and an elderly woman who got off in panic from the burning vehicle was hit by a car in the street, dying in hospital, the channel said.
Two more bodies were recovered after police removed the wreckage of the bus, which crashed into a truck while manoeuvering to escape the hit, it said. Another woman passenger was seriously injured.
Youths have been fighting street battles for days with police in the region's main city, Diyarbakir. On Saturday, there were clashes in Silopi, near the Iraqi border.
Protesters clashed with police in
Istanbul on Sunday
Locals gathered under a canopy in Kiziltepe to express condolences to relatives of the two men killed in the town.
Abdulkadir, a car salesman, said: "The people are very angry and I think the trouble will continue. We are protesting because we want Europe to know what is happening. How can Turkey enter the EU when it is like this?"
Erdogan has promised firm action to thwart those he says seek to divide Turkey.
State-run Anatolian news agency said a total of 565 protesters were detained and 247 of them formally arrested on Sunday, bringing to 445 the total number of arrests in two days.
Political analysts and diplomats say the violence reflects local anger over high unemployment, poverty and Ankara's reluctance to grant more autonomy to the mainly Kurdish region.
Locals expect more from Turkey's
EU accession talks
Locals are disappointed more reforms have not emerged out of Turkey securing an EU go-ahead last October to begin accession talks, and pledges of economic improvements by Erdogan.
Ankara has lifted restrictions on the Kurdish language and culture in recent years, hoping to further its bid to join the EU, but critics say it needs to do much more.