The fighting on Wednesday was the worst street fighting in the region in a decade and began after the funerals of four Kurdish fighters who were killed in fighting with Turkish soldiers.
The provincial governor said that between 2500 and 3000 Kurds rioted in Diyarbakir, the largest city in the overwhelmingly Kurdish region, damaging government offices, private businesses and banks.
He said three protesters were killed, one of them in a traffic accident while trying to escape, without saying how the others died.
Turkey's regional governors are state-appointed, and are in charge of local security.
Mayor Osman Baydemir, from the pro-Kurdish Democratic Society party, said two rioters were killed by gunfire and many others suffered injuries from gunshots.
Baydemir called on security forces to withdraw from the streets to prevent further rioting.
The four dead Kurdish fighters, whose funerals ignited the riots, were among 14 killed by soldiers in the province of Mus in a two-day clash that ended on Saturday.
They belonged to the Kurdistan Workers party, which has been fighting for autonomy since 1984.
Tensions have been running high in the southeast after Kurdish fighters escalated their attacks recently.
On Tuesday, thousands of protesters hurled firebombs at armoured police vehicles and smashed windows at a police station.
Fight for autonomy
The fight for autonomy, which began in 1984, has killed more than 37,000 people. The Kurdistan Workers party is considered a terrorist organisation by Turkey, the United States and the European Union.
Turkey is under pressure from the EU, which it wants to join, to grant more rights to its sizable Kurdish population, which it recognises as an official minority.
But Ankara has ruled out any dialogue with the fighters.
Meanwhile, Namik Tan, a foreign ministry spokesman, urged Denmark to shut down a Danish-based Kurdish satellite television station, Roj TV, which reportedly encouraged the rioters during Tuesday's clashes in Diyarbakir.
Turkey accuses Roj TV of being a mouthpiece for the Kurdistan Workers party. Danish authorities say they were still investigating, while Roj TV says it had no links to the fighters.