In the aftermath of Sunday's parade, 159 people were injured, many of them police officers, and 249 others were arrested, B92 Radio reported.
About 5,600 police officers were called out to protect marchers, and arrests continued overnight as protesters broke windows, looted stores and set fires, officials said.
"Policemen who took part are saying that they perhaps have not faced this amount of hatred and conflict for as long as they've been doing their job," said Interior Minister Ivica Dacic, who visited injured police officers in a hospital.
Authorities said 11 police vehicles and three fire trucks were damaged at different locations in the city, and that demonstrators started assembling long before the parade took place.
Protesters set fire to the Democratic Party's headquarters; junked offices occupied by the Socialist Party, and attacked the Belgrade mosque and several embassies, the report said.
The violence lasted for hours as police used teargas and armored vehicles to disperse crowds, and downtown Belgrade was closed for traffic until Sunday afternoon.
Among those taken in for questioning was Mladen Obradovic, leader of the right-wing group Obraz.
Organizers tried unsuccessfully to hold the parade in two previous years, the report said.