The Bianconeri boss had reacted angrily to the defender's inclusion in the Azzurri squad, claiming that Chiellini was not fit to feature at the Vicente Calderon given the 29-year-old had been sidelined for three weeks with a calf injury before being named on the bench for Sunday's Serie A win at AC Milan.
Conte claimed that Prandelli had been guilty of showing him a lack of courtesy by picking Chiellini, who did not feature at San Siro, but the Italy boss says he has done absolutely nothing wrong.
"We keep in close contact with all the coaches," the 56-year-old told reporters at the launch of the Azzurri's new PUMA strip in Milan on Monday. "We have been given maximum availability.
"Our medics are in contact with the medics of the clubs two weeks before the squad announcement. If a player is on the bench with his club, I have the right to call him up.
"The Juve medic sent a text to the national team's medic saying that all of his players were fine.
"It's also our last friendly before the World Cup. It is important to be here even if you're not playing."
Prandelli also said that he remains available to discuss the issue if either Conte or Juventus director general Giuseppe Marotta are seeking any further explanation for Chiellini's call-up.
"When Marotta has a problem, he can call me and I always respond," the former Fiorentina coach stated. "I was expecting a call from them."
For more information on Italy's 2014 World Cup strip: https://www.puma.com/footballclub