"The truth is that my colleague Giorgio Chiellini suffered the physical result of a bite in the collision he suffered with me. For this: I deeply regret what occurred. I apologize to Giorgio Chiellini and the entire football family. I vow to the public that there will never again be another incident like."
Suarez has previously been punished for biting during games in 2010 and 2013.
Chiellini, who has said that he thought FIFA's punishment was too harsh, responded to Suarez on Twitter.
"It's all forgotten. I hope FIFA will reduce your suspension," Chiellini wrote.
My apologies to Chiellini: pic.twitter.com/CvfkkjxzlM— Luis Suarez (@luis16suarez) June 30, 2014