Serbia police hold 19 over Genoa riots
They were arrested immediately after they entered Serbia and two more buses taking fans back from the Italian port were being searched, Ivica Dacic told Serbia's B92 television.
Italian police arrested 17 fans after Tuesday's Group C match between hosts Italy and Serbia was first delayed for 35 minutes and then abandoned after six minutes of play.
Having attacked their own goalkeeper before the match in an incident related to domestic club rivalry, Serbian fans threw flares on to the pitch and at Italian supporters in the Luigi Ferraris stadium.
Ivan Bogdanov, the alleged ringleader of the rioters who climbed a fence and ripped a hole in security netting to allow the flares to get through, was one of the 17 arrested in Italy having been spotted by police because of his distinctive tattoos.
Bogdanov, who will appear in court on Friday, apologised to Italy.
"My protest was against a director of the Serbian FA, I will say more in front of the judge," he said in a statement.
"I am nationalistic like everyone and a big fan of Red Star and I was also angry with the keeper who is now at Partizan.
"I say sorry to Italy, it's the first time I came to your country. I have nothing against it and did not expect this."
Serbia are waiting to hear what punishment they may face from UEFA while Italian officials have defended their role.
Interior Minister Roberto Maroni has urged the Europe-wide use of electronic cards for all travelling supporters which log movements and help better track potential troublemakers.
The introduction of the cards in Italy has been unpopular.
The violence in Genoa came two days after a mass riot in Serbia's capital Belgrade, where hooligans clashed with riot police in an attempt to disrupt a gay parade.
Political analysts in Serbia believe that incident involved a number of football fans affiliated with far-right groups.
Dacic did not rule out that the events were linked.
"These events are complementary and come from the same social background but there is not enough information that they were organised by the same people," Dacic said.
Serbian soccer has been rife with violence over the past 20 years, with clashes between rival fans resulting in several deaths and hundreds if not thousands of serious injuries.
Belgrade derbies between Red Star and Partizan have been at the core of the problem and riot police are likely to be deployed in numbers for the league fixture on October 23.