Defender Chiellini was ruled out of Tuesday's Euro 2016 qualifier against Norway due to a calf strain, having also missed a friendly victory over the Netherlands on Thursday.
Italy team manager Oriali expressed his disappointment that Juve had performed "a sudden U-turn" in not allowing Chiellini to remain with the national team until the end of the international break.
Juve responded on Saturday by stating that it was common sense for Chiellini to return to Turin.
Following recent events relating to Giorgio Chiellini's release from the Italian national team, Juventus Football Club would like to reiterate its ongoing commitment to working with the FIGC [Italian Football Federation], as it has done for more than a century," read a statement on the club's official website.
"Yesterday's announcement regarding the player's release and the insinuating remarks made by team manager Gabriele Oriali this afternoon do not alter this position.
"Our obligation to supporting the national team cannot run contrary to common sense or the rehabilitation needs of an injured player who is unavailable for the forthcoming Euro 2016 qualifying match with Norway which concludes the national team's commitments."
