The boy's funeral takes place later today, and police are bracing for more violence.
Prime Minister Costas Karamanlis has vowed to end the country's worst unrest in decades, but a government spokesman denied reports that they planned to declare martial law.
The unrest has left dozens injured and hundreds of buildings destroyed or badly damaged across the country. Greeks abroad also staged demonstrations in London, where five people were arrested, Berlin and Nicosia.
Ten people were treated in Athens hospitals for respiratory troubles caused by the blanket of tear gas over the city as the third day of battles for control of the streets went on into the night Monday, a health ministry spokesman said.
In the capital, protesters stoned the interior ministry, attacked police stations and clashed with riot police outside parliament.
They also set alight a major department store in the centre of the city and torched the official Christmas tree outside parliament.
There were street battles from Thessoliniki in the north to Crete in the south, with youths yelling "Cops! Pigs! Murderers!" at police.
Mr Karamanlis has vowed to end the riots, saying they were organised by extremists.
"All the dangerous and unacceptable events that occurred because of the emotions that followed the tragic incident cannot and will not be tolerated," he said.
The shooting of Alexandros Grigoropoulos, 15, was the catalyst for the violence, but it comes against a background of high youth unemployment, the rising cost of living, stalled pension reform and a widening gap between rich and poor.
The centre-right government is accused of doing little to help low-income Greeks who are in the grip of the financial crisis.
The government has also been criticised for a 28-billion-euro liquidity support package for Greek banks struggling to cope with the credit crunch - many Greeks feel that the banks do not need, or deserve, the money.
The riots are some of the worst Greece has experienced since the country's military dictatorship was toppled in 1974.
They began within hours of the teenager's shooting on Saturday night in the bohemian but often volatile Athens district of Exarchia. Two police officers have been arrested and one has been charged with murder.
About 30 civilians have been treated for minor injuries in hospitals around the country and Athens police said 37 policemen were hurt in the capital over the weekend.
Running battles between riot police firing tear gas and about 400 secondary school students throwing rocks broke out on Monday in Veria, a town about 40 miles west of the port city of Thessaloniki.
In Chania, a Crete town popular with British holidaymakers, gangs of school students threw broken chairs, rocks and pieces of wood at riot police, who responded with tear gas.
On Rhodes, students pelted a local police station with various projectiles, prompting officers to fire tear gas.
Fierce debate swirled around the circumstances of the teenager's death. The officer accused of the shooting said he fired warning shots to scare off a gang of youths and that the bullet ricocheted off the pavement, but witnesses told Greek reporters that he deliberately took aim at the boy.
Mr Karamanlis' increasingly unpopular conservatives have a majority of one seat in the 300-member Parliament. The opposition Socialists are ahead in opinion polls for the first time in eight years.
Greece is bracing for more violence on Wednesday, when a nationwide strike over pension reform and the government's lacklustre response to the financial crisis are expected to bring the country to a standstill.
All flights in and out of the country will be stopped.
The unrest spread to Greek diplomatic missions abroad. In London, demonstrators pulled down the Greek flag, set it ablaze and raised the red-and-black anarchists' banner at the Greek Embassy.
Police officers were forced to block off the street and arrested five people.
In Berlin, 15 youths occupied the Greek consulate, raising a banner describing the shooting as "murder".
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