Over 20,000 people made the traditional march from the National Technical University of Athens, site of the 1973 uprising, to the US Embassy on Sunday.

Police said about 10,000 people participated in a Communist Party rally and a further 1000 marched with the formerly ruling leftist Syriza party, both separate from the main march with over 10,000 participants.

Former Prime Minister Alexis Tsipras started the march with Syriza but left before the halfway point.

Police say they arrested 28 people in clashes after the march, mostly in the Exarchia neighbourhood near the university, and detained a further 13.

A recent crackdown by the conservative government on extreme leftist activity in Exarchia, a known anarchist haven and counterculture centre, and another nearby university, the Athens University of Economics and Business, had raised fears of possible heavy clashes.

More than 5000 officers were deployed, focused on preventing rioters from occupying the rooftops of apartment buildings and hurling firebombs and rocks into the streets below, as happened two years ago.

Police tactics appeared to have worked, and the first six arrests, shortly after the march, were of people who had sneaked firebombs, rocks, gas masks and other paraphernalia onto a rooftop close to Exarchia's main square.

There were reports of police violence, including from a news site reporter who said he was attacked while filming riot police pursuing protesters. He appeared in a video with his face bruised.

Clashes with police also took place in the northern city of Thessaloniki, again after marches in which almost 10,000 took part, as well as in other Greek cities.

In Thessaloniki, vehicles were set on fire. Local police said they had detained more than 10 people.

Australian Associated Press