Pasok's youth wing has called for peaceful protests.
Most of the clashes have occurred in university cities and have involved students, says the BBC's Malcolm Brabant in Athens.
The student demonstrators have been given tacit consent to continue by their professors, our correspondent says.
University tutors said they would start a three-day walkout on Monday, rather than joining a nationwide workers' strike against pension reforms and economic policies on Wednesday.
Although the protests began as an outpouring of anger about the killing, they appear to have become more politically motivated, with opposition parties keen to discredit the struggling government, our correspondent adds.
The government has held an emergency meeting to decide how to respond, with the Interior Minister, Prokopis Pavlopoulos, saying the police would adopt a defensive stance.
The riots began on Saturday after Alexandros Grigoropoulos was shot dead by police in the Exarchia area of Athens.
The unrest, the worst in the country in several years, later spread to Thessaloniki, Patras, Larissa, and Volos, and the islands of Crete, Samos and Corfu.
Dozens of protesters and police have been injured during pitched battles on the streets, involving petrol bombs and tear gas.
A march by more than 1,000 people on two police stations in Thessaloniki descended into violence when protesters attacked police and shops with firebombs and rocks.
Prime Minister Costas Karamanlis has written to the boy's parents expressing his profound sorrow.
He wrote: "In these difficult moments please accept my condolences for the unfair loss of your son. Like all Greeks I am deeply saddened."
He said his government would act to stop "such a tragedy" from happening again.
MAIN LOCATIONS OF ATHENS PROTESTS
Thousands of students, leftist demonstrators and anarchists on Sunday marched from the National Archaeological Museum and Polytechnic on Patission Avenue towards the police headquarters on Alexandras Avenue
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