"The recent events call for urgent action," said Serbian Sports Minister Alisa Maric, who also urged restraint in punishing the national federation for the incidents during Tuesday's match.
Serbia was charged by UEFA on Wednesday with misconduct over racial abuse its fans allegedly hurled at England players from before kickoff in Krusevac. Both federations also face sanctions over a brawl between the teams that erupted after the European Under-21 Championship qualifying match that England won 1-0 with an injury-time goal.
The Serbian football federation has denied racism allegations during the match, but the English Football Association insisted its players were subjected to racial abuse, missiles and provocation throughout the game. England said it might stop sending teams to Serbia.
But Serbia U-21 coach Aleksandar Jankovic said the English are overreacting.
"They started this claim of racism because that's the most sensitive issue," Jankovic told Vecernje Novosti newspaper. "I did not see racism in Krusevac, and I was there on the field from the first minute (of the match) to the last second of the brawl.
"There is no excuse for what happened ... but the English are now acting as if they are innocent, and they are not," Jankovic said.
England defender Danny Rose has complained that he was subjected to monkey chants throughout the match. He was sent off after kicking a ball into the stands after the final whistle following apparent provocation, gesturing to the crowd that he was racially abused.
Serbia midfielder Nikola Ninkovic, who chased Rose at the end of the match, said the England defender was the instigator of the incidents.
"The guy made inappropriate gestures towards our fans three or four times," Ninkovic said. "His behaviour annoyed me, but I know I was wrong (for pushing Rose) and I know I will be punished. I just hope it will not be too harsh."
The Serbian federation's disciplinary committee said Thursday it is collecting statements from its players and coaches and will decide who will be punished for taking part in the post-match brawl.
Associated Press writer Jovana Gec contributed to this report.