Fare executive director Piara Powar says its report to FIFA identifies Germany, France and Belgium fans who have worn black face make-up during matches.
Images of at least two Germany fans appeared on social media with blackened faces at the team's match against Ghana.
Fare says in a message posted on its Twitter account that it also advised FIFA about a pitch invader in that match "with neo-Nazi references painted on his body."
In a separate incident involving a Colombia fan, Fare reports "a man wearing a clerical costume daubed with swastikas."