The situation escalated as hundreds of young people joined the protest, throwing stones and bottles at lines of riot police, who responded with tear gas.
Police used tear gas to disperse stone-throwing protesters
In the afternoon thousands of mourners gathered for the teenager's funeral in a coastal suburb further south.
The ceremony was calm, but violence then erupted outside the cemetery. Police used tear gas against groups of youths who threw stones and set rubbish bins ablaze.
By late evening, 15,000 police were deployed in the capital to maintain control, Reuters news agency said.
There was more fighting elsewhere in the country too.
In Thessaloniki, police clashed with groups of young people following a protest march earlier in the day. In Patras, a western port, rioters armed with petrol bombs and stones attacked the main police station.
Two police officers have been charged in connection with Alexandros Grigoropoulos's death, but results of a post-mortem to determine the trajectory of the bullet that killed him are not yet known.
The officer who fired says it was a ricochet from a warning shot but witnesses told Greek TV he fired directly at the teenager.
In Athens, Prime Minister Costas Karamanlis held talks with President Karolos Papoulias and opposition leaders to discuss what action to take.
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