Story highlights President Barack Obama talks about democracy in a speech near the Acropolis

Police: Anarchists became violent after they tried to break through a police cordon

Athens, Greece (CNN) Six people have been arrested in the Greek capital after a group of anarchists started throwing rocks and Molotov cocktails following an anti-capitalism protest, Athens police told CNN.

Protesters stand in front of graffiti that reads "No Hope" on Tuesday in Athens.

The arrests occurred Tuesday after a peaceful demonstration, organized by the Communist Party and permitted by police, in Omonia Square near central Athens.

About 5,000 people attended the anti-establishment protest, police said. After it was over, a group of some 100 to 150 anarchists became violent, police said.

Police look at flames from a fire bomb thrown by demonstrators Tuesday.

Unrest broke out as the group tried to break through a police cordon to march to the US Embassy and Presidential Mansion, where Obama was attending an official state dinner.

Read More