The Greek government has held an emergency meeting to consider its response to continued violent rioting across the country.
Rioters clashed with police for a third day on Monday, in protests which erupted after a 15-year-old boy was shot and killed by police on Saturday.
A funeral for the boy, Alexandros Grigoropoulos,is being held on Tuesday.
Appeals for calm have so far been largely ignored by the mostly young protesters in Greek towns and cities.
Dozens of people have been injured throughout the country and there are reports of looting in some areas.
Greek Prime Minister Costas Karamanlis has appealed for calm, saying the government was obliged to protect the community.
"The unacceptable and dangerous events that have gone on under the most extreme of emotions cannot and most not be tolerated," he said, and called for a sense of solidarity with the dead boy's family.
Mr Karamanlis is due to meet President Karolos Papoulias on Tuesday morning and will also consult the leader of every opposition party in an attempt to reach a consensus on what action to take.
But the BBC's Malcolm Brabant in the capital Athens said police appeared to be powerless to prevent rioters from attacking symbols of wealth and prestige.
The city's giant Christmas tree in central Syntagma Square was set on fire and windows were smashed on hotels, banks, government buildings and departments stores.
Police used teargas against protesters throwing petrol bombs and setting fire to buildings, vehicles and rubbish bins.
"Rage is what I feel for what has happened, rage," said a student taking part in the protests.
"This cop who did it must see what is to kill a kid and to destroy a life."
Siran Zebaharian, whose shop was damaged, said police arrived too late to protect her business from rioters.
"They were battering the windows with terrible force, attacking passing cars, throwing petrol bombs at parked jeeps," she said.
Violent clashes were also seen across the country, with rioting reported in the central city of Trikala and police stations attacked in Piraeus and Corfu.
Hundreds of students clashed with riot police in Thessaloniki, Greece's second biggest city, where students used university buildings to stockpile petrol bombs.
Photo journalist Vassiliki Polychronopoulou told the BBC that the teenager's death had acted as a spark for protests over a range of frustrations.
"The government they don't seem to be able to control anything at all in terms of economics, in terms of social changes," she said.
"People have lost their faith in everything."
Mr Karamanlis has blamed "extreme elements" for taking advantage of the situation to engage in vandalism.
He has pledged to compensate businesses damaged.
As he left the emergency cabinet meeting, Greece's Interior Minister Prokopis Pavlopoulos said the unrest was "unacceptable" and would not be tolerated, but did not say what the government's plans were to handle the crisis.
Mr Pavlopoulos said police were handling the violence well. he said "not a single life" was in danger and that protecting life was more important than protecting property.
Observers say a state of emergency may be imposed, giving the authorities special powers to clear the streets.
But there is no question of calling in troops. Greece has bitter memories of military rule so seeing troops on streets would be beyond the pale, says our correspondent.
The authorities fear there could be further unrest when Alexandros Grigoropoulos, the boy whose death initiated the protests, is buried on Tuesday.
Witnesses say Alexandros was killed by a direct hit from a bullet
A post-mortem has been carried out on his body to determine the trajectory of the bullet that killed him. The results are not yet known.
Two police officers have been arrested in connection with the incident.
The officer who fired contends it was a ricochet from a warning shot, but witnesses told Greek TV it was a direct hit.
The boy's family has hired an independent pathologist to ensure there is no cover-up.
On Sunday, the prime minister wrote to the boy's parents: "In these difficult moments please accept my condolences for the unfair loss of your son. Like all Greeks I am deeply saddened."
However, analysts say nothing the politicians or authorities can say or do is likely to reduce the anger that is building.
A similar shooting incident in 1985 led to a lengthy vendetta between the youths and police, with violence continuing for years.