A 22-year-old man died in fighting between two groups of youths as police fired water cannons and tear gas to prevent crowds from reaching Istanbul's main square after the burial of 15-year old Berkin Elvan.
In the south-eastern city of Tunceli, a policeman died of a heart attack in clashes with anti-government protesters.
Officials denied reports that tear gas fired by police had triggered the heart attack, insisting the officer had not been exposed to gas.
Anti-government protests have flared since the death of the teenager on Tuesday.
He had been in a coma since being injured last May.
Prime Minister Tayyip Erdogan accused the protesters of trying to sow chaos to influence local elections.
He said: "You were supposed to be democrats, pro-freedom. These are charlatans, they have nothing to do with democracy, they do not believe in the ballot box.
"They are saying let's cause chaos and maybe we'll get a result. But my brothers in Ankara and Turkey will give the necessary answer on March 30 (in the local polls)."
Mr Erdogan claimed the clashes and a corruption scandal dogging his administration are part of an anti-government plot.