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Belgrade Mayor Dragan Djilas said damage was estimated at more than 1 million euros ($1.39 million).

Right-wing groups say the gay events run counter to Serbian family and religious values. Most of the rioters Sunday were young football fans whose groups have been infiltrated by neo-Nazi and other extremist organizations.

“These riots obviously have nothing to do with the gay parade or any moral values,” Democratic Party spokeswoman Jelana Trivan said. “These are hooligan gangs which must be punished severely.”

Defense Minister Dragan Sutanovac, vice president of the Democratic Party, said a part of the party’s archive, warehouse and phone lines at the building were destroyed and shots also were fired at the building.

“It is high time that we deal in a very democratic way, through the courts, with those who call themselves members of the patriotic organizations,” Mr. Sutanovac said. “Is this Belgrade or the wild West?”

Senior Justice Ministry official Slobodan Homen said the state response would be “fierce.” He said the city center is covered with surveillance cameras, the rioters have been identified, and many already have been detained. He said they could face up to eight years in prison.

Vincent Degert, the head of the EU mission in Serbia, addressed about 1,000 gay activists and their supporters who gathered at a park in downtown Belgrade that was surrounded by riot police, including some in armored vehicles.

“We are here to celebrate this very important day … to celebrate the values of tolerance, freedom of expression and assembly,” Mr. Degert told the crowd, members of which waved rainbow flags.

The same right-wing group set the U.S. Embassy on fire during riots in 2008 to protest U.S. support for Kosovo’s independence.

U.S. Secretary of State Hillary Rodham Clinton plans to visit Belgrade in the coming days as part of a tour of the Balkans.