Police said they made nine arrests while 15 officers were injured, and the health ministry said a reporter and two teenage girls were treated for bruises.
The violence first broke out as hundreds of pupils took part in a midday demonstration to mark the December 6, 2008 death of Alexis Grigoropoulos, followed by new clashes at an evening protest by students and leftist groups.
The security forces used tear gas and stun grenades to disperse protesters who pelted them with firebombs and stones.
Although police said approximately 2000 people took part in the follow-up protest, an AFP photographer put the turnout at more than 4000.
ANGER OVER AUSTERITY BUDGET
Some 1500 school pupils had earlier protested outside parliament as the assembly completed a five-day debate on a new austerity budget headed for a vote after midnight.
Television footage showed small groups of protesters throwing stones and firebombs at riot police on the plaza below the parliament building and next to the Greek war memorial.
The demonstrators carried banners against the government's tough austerity measures and against the police.
"Money for the banks, bullets for the young, three years after the state assassination," one banner read.
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