FIFA hit Suarez with a nine-game international ban and suspended him from all football-related activity for four months after he bit Giorgio Chiellini in Uruguay's 1-0 win over Italy on Tuesday.
The victory booked Uruguay's place in the last 16, but they look set to be without their talisman - who has been involved in two previous incidents of biting an opponent - for the remainder of the tournament.
However, AUF chief Wilmar Valdez has now announced their intention to appeal the governing body's decision.
"We respect the decision of the disciplinary body, but there is not strong enough evidence for a sanction of this kind," Valdez is quoted as saying by various media outlets.
"It feels like Uruguay has been thrown out of the World Cup."
Uruguay's first game without Liverpool forward Suarez takes place on Saturday in their second-round clash with Colombia at the Maracana in Rio de Janeiro.
