More than 10 police stations, from the coastal suburbs to western working class districts, were attacked within one hour.
Stones and firebombs were used in the clashes, with one elderly bystander injured.
Police also clashed with demonstrators and groups of looters outside the country's biggest prison and a university in central Athens.
Clashes occurred at Koyrdallos prison in a western Athens suburb after protesters threw rocks and other missiles at police, who fired tear gas to force the protesters back, a prison guard said.
Demonstrators later staged a sit-down protest in front of the prison amid more confrontations with security forces.
Police said there was also unrest at the Athens agriculture university, which has been occupied by students, and that youths were attacking stores in the upmarket Nea Smyrni and Galatsi districts of the capital.
School and university students and teachers have called a rally in Athens tomorrow and further demonstrations are planned for next week.
More than 100 schools and some 15 university campuses remain occupied by youth demonstrators in Athens and the second city of Thessaloniki.
The shooting of 15-year-old Alexandros Grigoropoulos ignited anger at police brutality and rising economic hardships due to the global economic slowdown.
Many people are angry that the 37-year-old policeman charged with murdering the teenager did not express remorse to investigators on Wednesday.
He said he fired warning shots in self-defence which ricocheted to kill the youth.
Epaminondas Korkoneas and his partner, who is charged as an accomplice, were detained pending trial by a prosecutor on Wednesday.
Lawyers for the men claim tests on the bullet which killed the teenager showed it had ricocheted.
Prime Minister Costas Karamanlis, who has announced financial support for hundreds of businesses damaged in the rioting, travelled to Brussels for an EU summit today, as the government tried to carry on business as usual.
Mr Karamanlis and opposition leader George Papandreou appealed for an end to the violence, which hit at least 10 Greek cities and damaged hundreds of millions of euros in property.
Greeks also protested in Paris, Berlin, London, Rome, The Hague, Moscow, New York, Italy and Cyprus.
