Rostov coach Igor Gamula said Friday the club had "enough dark-skinned players, we've got six of the things" when asked about rumours Rostov could sign a defender from Cameroon.
According to soccer agent Paul Mitchell, five African players on the team threatened to sit out Monday's training. Mitchell is the agent of Rostov defender Siyanda Xulu, a South Africa international.
"(They are) not prepared to train under the current coach," Mitchell told The Associated Press.
However, Gamula told Russian agency Tass that he apologized to the team on Monday and that all the players had taken part in training.
"I've never divided players into good or bad, foreigners or Russians," Gamula said, adding he had been "in shock" at the reception his comments had received. "I was deeply worried and didn't sleep for two days. I hadn't wanted to insult or upset anyone."
The Russian Football Union could not be reached for comment.
Rostov will be a host city at the 2018 World Cup, and Mitchell said Gamula's comments will cast a shadow over the southern city.
"If Rostov were to keep somebody in that position who's come out and said something like that, then I think it would be very damaging to them as a city going on to the World Cup in 2018," Mitchell said. "We don't think he should be in his job."
Rostov won the Russian Cup last season, but has struggled this season, sitting 14th in the Russian league and exiting the Europa League in the final qualifying round.
Rostov's squad has five African players, from South Africa, Angola, Mali, Gabon and Ivory Coast. The club is owned by the city government.
Historically, the city of Rostov has one of Russia's largest African populations, many of them students given scholarships to local universities.
Racism is not uncommon at Russian football matches. Last year, Manchester City midfielder Yaya Toure said black players could boycott the World Cup if racism at matches was not reduced. He spoke after being racially abused by CSKA Moscow fans in a Champions League game.