Tahir Elci, head of the bar association in Diyarbakir -- the biggest city in the mainly Kurdish southeast -- and a campaigner for Kurdish rights, was shot in the head while he and other activists were giving a press statement calling for an end to violence.
The attack took place near an ancient mosque in the city's Sur district, witnesses told AFP, with the police immediately returning fire.
Police also clashed with demonstrators at Diyarbakir, an AFP photographer said.
Elci, who had been detained in October for alleged "terrorist propaganda" on behalf of the outlawed Kurdistan Workers' Party (PKK), was killed by a single bullet to his head, the autopsy showed.
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The office of the Diyarbakir governor said one policeman was also killed and two others were injured.
"The speech was over and we were dispersing. Then we heard one or two gunshots from the street. Police immediately reached for their guns and people hid wherever they could," Nazim Baran Vurak, a lawyer, said.
"Then our friends told us that a man was lying face down on the street and he looked a lot like Tahir Elci."
Two more police officers tasked with protecting the prosecutors inspecting the crime scene were injured after coming under rocket fire, an AFP reporter said.
"One possibility is that after this terror attack, the assailants assassinated Mr. Elci," Davutoglu said. "A second possibility is that ... Elci got caught in the crossfire."
A manhunt was underway while clashes were continuing throughout the Sur district, where authorities have declared a curfew, an AFP correspondent reported.
The state-run Anatolia news agency claimed that members of the PKK were behind the incident, while the Dogan news agency, quoting witnesses, said a bearded man had opened fire on the group.