The BBC's Malcolm Brabant, in Athens, says that the rioters have set fire to banks and stores in the city's main shopping district. A four-storey building has also been torched and many cars destroyed.
Greece's anarchists regard the quarter of Exarchia as their fortress and they frequently lure police into ambushes so they can attack them with rocks and fire bombs, our correspondent says.
As dawn broke over the city, emergency crews were damping down fires while many of the youths were understood to have retreated to Athens Polytechnic.
There are no reports of casualties among the police or rioters.
In a statement, interior minister Prokopis Pavlopoulos expressed the government's "profound regret" for the shooting of the boy, reported to be 16-years old.
"An inquiry on the circumstances of the death has already begun and, if the policemen are found to have been derelict in their duty, the punishment will be exemplary."
In Athens, police fired tear gas at hundreds of stone-throwing youths, who went on a rampage as news of the shooting spread.
After a lull of a couple of hours, rioting resumed shortly after midnight local time (2200 GMT), with some protesters marching through Athens city centre and others fighting police outside the National Technical University of Athens, the Associated Press news agency reported.
Although damage was widespread, there were no reports of looting.
Witnesses said that the destruction was not indiscriminate. While clothing shops and banks were badly damaged, the numerous snack bars were all left intact.
Vassilis Papadopoulos, who owns a shop that was badly damaged in the rioting, said the timing was particularly bad.
"It happened just before Christmas, we made an effort to decorate it, now the staff will come and see this," he said.
Many cars have been destroyed in the Athens riots
"Where will they get their Christmas bonus and Christmas gift from now? Its completely damaged, its tragic."
In Thessaloniki dozens of youths attacked a police precinct, while others blocked a road near the university campus.
People were being encouraged to join in the protests via some websites, AP said.
An Interior Ministry press officer told Reuters news agency that Mr Pavlopoulos had offered his resignation to Prime Minister Costas Karamanlis, but it had been rejected.
Police issued a statement after the shooting, saying a patrol car with two officers inside was attacked by about 30 youths throwing stones.
They were attacked again and responded, with one firing a stun grenade and the other shooting and fatally wounding the boy, AP quoted the statement as saying.
Correspondents say the shooting and rioting are certain to ramp up clashes between anarchists and police.
A similar shooting in 1985 led to years of violence.
Residents have recently protested over rising crime and lawlessness, and complain that the police fail to answer emergency calls, staying barricaded in their police stations, our correspondent adds.
There were clashes between students and police in Athens last week when about 4,000 people attended a rally to oppose education reforms.
Police made 12 arrests after a group of violent protesters broke away and damaged banks and shop fronts.
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