“HNS hereby apologizes to the Russian public for the actions of a member of the Croatian delegation,” it said.
It said that Vukojevic and Vida also apologized for their statements, saying they were not intended to be political messages but “unfortunately left room for such interpretations”.
Both Vukojevic and the 29-year-old Vida previously played for Ukrainian club Dynamo Kiev.
Croatia face England in the semifinals of the tournament in Moscow on Wednesday.
Questions on the subject were not allowed when Croatia players Mario Mandzukic and Andrej Kramaric spoke at a news conference in Moscow later on Monday.
“We have been quite clear on the matter, that is the position of the federation and we don’t need to ask the players,” a Croatia team spokesman said.