The protests in memory of Alexandros Grigoropoulos's death last Saturday in Exarchia had begun peacefully.
Students of the school the teenager had attended held a silent vigil during the day in Syntagma Square. Hours later, hundreds of others brought candles to the site, while others gathered at the site of the shooting.
But later, about 100 youths hurled volleys of petrol bombs and rocks at a police station in the Exarchia district, where the officer, who shot him and has now been charged with murder, was based. The protesters chanted "murderers out".
Wearing hoods and masks, the protesters then turned their attention to a commercial area near the National Technical University of Athens, known as the Polytechnic, overturning cars and setting fire to three banks. Several shops and an office of the environment ministry were also attacked.
Riot police positioned at street corners in the area responded by firing tear gas at the protesters.
Several restaurants in Exarchia had already closed early in anticipation of the violence. Many shop owners meanwhile boarded up their windows as night fell.
Police subsequently charged the vigil in nearby Syntagma Square, when those taking part refused to move further away from the parliament building and the Tomb of the Unknown Soldier.
Meanwhile in Greece's second city of Thessaloniki, dozens of youths vandalised a gymnasium during a demonstration, according to the AFP news agency.
Our correspondent says anger at the killing of the teenager has developed into a widespread sense of anger at Greece's government over the past week.
Some semblance of calm had returned to Athens on Saturday
Thousands of Greeks have taken to the streets across the country, repeatedly clashing with police and vowing to overthrow the government.
Many have identified themselves as anarchists happy to use violence in what they say are legitimate protests against the government.
Some, though, have welcomed the return of a semblance of calm prior to the violence on Saturday evening. In Athens, Mayor Nikitas Kaklamanis greeted Christmas shoppers with the city's brass band.
"People came up to me and were telling me that it was the first time they had smiled in days," the mayor told the Associated Press.
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