Several other people have been seriously injured.
Promise of justice
The angry protests were sparked by a bomb at a bookstore in nearby Semdinli last week.
Three Turkish security officials have been charged in connection with the attack, thought to have been targeted at a member of the Kurdistan Workers Party, the PKK.
Since then the violence has rotated between towns in this mostly Kurdish area, close to the border with Iraq.
With little sign of any let-up in the unrest, Turkey's Prime Minister Recep Tayyip Erdogan chaired a four-hour meeting of security officials in Ankara.
In a statement afterwards, he repeated his promise that all those responsible for the original bombing would be revealed and brought to justice.
But the clashes in Hakkari are still going on and in nearby Yuksekova - where the three people died on Tuesday - tensions remain high.