The protests were sparked by the killing of 15-year-old Alexandros Grigoropoulos on December 6, but they fed on growing anger over political scandals, high youth unemployment and low wages, as well as the impact of a global recession on Greece's economy.
"It was expected this would continue for a second week," Kiki Toudoulidou, a teacher, said.
"If the government was handling the situation in the right way, we wouldn't have reached this point."
Further demonstrations are expected on Wednesday and Thursday, as students and teachers planned to take to the streets in protests at changes to the education and pensions systems, privatisations and tax rises.
The ruling New Democracy party of Costas Karamanlis, the prime minister, has denounced the riots as the work of a small group of hardcore anarchists, but at their peak early last week thousands of youths ran riot through 10 Greek cities, destroying hundreds of cars, banks and businesses.
Karamanlis, whose hands-off response to the riots has been criticised by the Greek media, travelled to Cyprus on Monday to attend the funeral of Tassos Papadopoulos, the former president.
The national confederation of commerce estimates that 565 shops have been damaged during the violence in Athens, damaging more than $250m worth of assets.
Many shoppers stayed away away from the central of the capital on Monday, at a time when the streets would normally be crowded as Christamas approaches.
"There is no business. People are disappointed and angry," Dimitra, a shopowner who declined to give her second name, said. "The protests will continue. They only needed an excuse."
The policeman charged with killing Grigoropoulos has been jailed along with a colleague pending trial, while more than 400 protesters have been detained during the unrest.
Most of the demonstrators have been subsequently been released without charge.