The FIGC said in a statement they had "received late yesterday evening" Mancini's surprise decision to step down.
"Because of important and close commitments for the team with Euro 2024 qualifiers against North Macedonia and Ukraine, the FIGC will announce the name of the new national coach in the next few days," the federation added.
Mancini was appointed in May 2018 after Italy's failure to qualify for the 2018 World Cup under Gian Piero Ventura.
A former international, Mancini won Euro 2020 with Italy but then failed to qualify his side for the 2022 World Cup in Qatar.
Mancini's resignation comes as a major shock with no warning signs.
Earlier this month the 58-year-old had also been handed responsibility for the country's Under-21 and Under-20 teams.
The Italian press has speculated that Luciano Spalletti could be lined up as his successor after ending Napoli's 33-year wait for the Serie A title last season, before leaving his post.
