The protesters, mostly members of the Hungarian Self Defense Movement, were on the way to the Palace of Art, where Ferenc Gyurcsany, the prime minister, was participating in a commemoration event.
The police fired tear gas and dispersed the protesters, before they could reach the venue.
The Hungarian media reported that protesters also attacked a journalist covering the violence and that the clothes of two demonstrators caught fire, after being hit with a Molotov cocktail, that was aimed at police.
Police set up metal barriers around the Hungarian parliament and several other areas where official events were being held.
Peter Rabai, a 53-year-old Hungarian salesman attending one of the rallies, said: "The government has to go. They are ruining Hungary."
Demands for Gyurcsany's resignation intensified after Hungarians repealed three of his economic reform measures in a referendum held by Fidesz, the main opposition party.
Viktor Orban, the former prime minister of Hungary, said: Since the referendum, we know that Hungary deserves better."
Fidesz has often compared Gyurcsany's current government to that which served the interests of the Habsburgs 160 years ago.
In September 2006, protests and riots broke out after Gyurcsany was heard admitting on a leaked recording that he had lied for months about the economy, so as to win the April 2006 elections.