Uruguay striker Suarez was banned from all football-related activity by FIFA after biting Giorgio Chiellini during his country's World Cup clash with Italy last month.
Suarez was also suspended for nine international matches, with the Uruguayan Football Association's (AUF) initial appeal against those sanctions rejected.
However, Suarez's lawyer Alejandro Balbi has since confirmed the 27-year-old's decision to take the case to the Court of Arbitration for Sport (CAS).
Chiellini has forgiven Suarez for his actions and expressed his hope that the ban will be reduced.
And South American football's governing body CONMEBOL have now stated their intention to back Suarez, who signed for Barcelona from Liverpool this week.
A CONMEBOL statement read: "The decision in the case of Uruguayan national team player Luis Suarez was ratified in all respects by the Appeal Commission of the FIFA Disciplinary Committee on July 8.
"CONMEBOL and its ten member associations, while respecting the decisions of FIFA in respects to Uruguayan Luis Suarez, does not agree with them as the sanctions are excessive and disproportionate to the offense.
"From this point CONMEBOL wishes to express its full support and cooperation with the player and the Uruguayan Football Association if they decide to exhaust all existing appeals.
"Also, CONMEBOL through their representatives in the various bodies of FIFA will soon make concrete proposals to improve the performance of the disciplinary bodies of FIFA and avoid situations like this."
