No injuries or arrests were immediately reported.
Police said groups of hooded anarchists torched two banks, smashed shop windows and threw petrol bombs at police buses outside the capital's police headquarters before running off down side streets. A patrol car was also set on fire.
The clashes erupted as some 30,000 anti-globalization and anti-war demonstrators launched a peaceful march through the city center, the AP reports.
"We want jobs not bombs" read one of the many banners carried by marchers, who were expected to stop briefly outside the U.S. and British embassies before heading for central Syntagma Square.
The march was organized by the European Social Forum, which is holding a four-day meeting at a decommissioned airport on the outskirts of Athens.
More than 8,000 police have been on alert throughout the capital for the fourth European Social Forum, which ends Sunday.
The march, which also includes representatives of workers unions, left-wing groups and about 10,000 foreign activists, brought public transport services in central Athens to a halt, while shops shut down.
After it turned out that Deputy Prime Minister Andrei Belousov included the Fonbet betting company in the list of backbone enterprises that can count on state support, everyone started talking about these bookmakers.