Conte has been caught in a furore involving former team Juventus after club patron John Elkann reportedly blamed the national team coach's excessive training for the knee ligament injury sustained by Claudio Marchisio on Friday.
FIGC president Carlo Tavecchio stated that Conte feels he is being unfairly criticised and revealed he has been the subject of online death threats.
Speaking to Rai Sport, he said: "I saw him [and he was] shaken.
"After the controversy [with Juventus] he received death threats on the internet.
"He feels vilified for responsibilities that are not his fault. The FIGC stands by him."
Conte will be in the dugout when Italy take on Bulgaria in UEFA Euro 2016 qualifying Group H in Sofia on Saturday.
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