Six people were arrested, one of them for carrying a weapon.
Alex Hadjisavvas, the owner of a shop on Patission Avenue in central Athens, told the BBC businesses had been looted and the street resembled a "warzone".
"The window was smashed, the shop front damaged and a large quantity of stock taken from inside has been used by the rioters as material to start street fires," he said.
The unrest, the worst in the country in several years, later spread to Thessaloniki, Patras, and the islands of Crete and Corfu.
After a lull in the fighting on Sunday morning, youths left the National Technical University of Athens, known as the Polytechnic, and joined thousands of leftist demonstrators and anarchists on a march towards the police headquarters on Alexandras Avenue.
They passed close to where 15-year-old Alexandros Grigoropoulos was shot dead on Saturday. One banner called the police "murderers".
One protester told the BBC he had been greatly angered by the actions of the police.
"It's not the first time. They always kill people - immigrants, innocent people - and without any excuse," he said. "They murdered him in cold blood."
The unrest, the worst in several years, has spread throughout the country
"I think [the violence] is justified. Peaceful demonstrations cannot get a solution to the problem."
The march soon turned violent, with protesters chanting "killers in uniform" and throwing petrol bombs at riot police, who fired back tear gas.
Several banks and shops were attacked, while a car showroom was set alight, trapping people living in the floors above. Clashes also broke out near the parliament.
At least 34 people were injured as a result of the violence on Sunday, officials told the Reuters news agency. At least 10 demonstrators were detained.
As night fell, groups of protesters used rubbish bins and overturned cars to erect burning barricades in the streets around the Polytechnic, inside whose campus many have taken refuge in the knowledge that police are prohibited from entering.
The police said they planned to pull out of the area overnight in order to defuse tensions, although many officers were still deployed around the university late on Sunday.
Earlier, 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.
MAJOR RIOTING IN GREECE
1973 - Brutal repression of student uprising in Athens helps bring down the military junta
1985 - Youths clash with police in Athens after rally marking 1973 uprising becomes violent and police shoot dead 15-year-old boy
1991 - Riots break out across the country after a school teacher is killed during protests in Patras
1995 - Riots erupt after protest in Athens and revolt in prison ahead of 1973 uprising's anniversary
1999 - Police clash with protesters opposing a visit by US President Bill Clinton to Athens
2003 - Youths battle police during an EU summit in Thessaloniki
2008 - Protesters battle police across country after an officer shoots dead a teenager in Athens
There were unconfirmed reports that a policeman was injured and banks and cars set on fire during protests in the western port of Patras. Clashes were also reported on the islands of Crete and Corfu.
The BBC's Malcolm Brabant in Athens says Greece's conservative government, which is currently reeling from a series of scandals and economic troubles, is desperately trying to calm the situation.
Prime Minister Costas Karamanlis has written to Andreas Grigoropoulos's parents expressing his profound sorrow.
Interior Minister Prokopis Pavlopoulos, whose offer to resign was refused by the prime minister, has urged both protesters and police to act with restraint.
The two police officers involved in the shooting of the teenager have been arrested, and an inquiry is under way.
In a statement, the police said their patrol car had been attacked by about 30 youths and responded, with one officer firing a stun grenade and another shooting and fatally wounding the boy.
However, our correspondent says that 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.
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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