The 53-year-old has been handed the daunting task of lifting Italy out of the doldrums after their failure to qualify for this year's World Cup, the first time they will miss the tournament in 60 years.
The four-times world champions have also slumped to a record low of 20th in the FIFA rankings.
"I would like to be the coach who brings Italy back to the top. It will not be easy but we can do it," he said, suggesting that he would aim to win Euro 2020.
"We have not won the European championship for many years and that is our first big event."
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Remembering that he first walked through the doors of Italy's Coverciano training camp in 1978 with the under-14 team, Mancini said it was the right moment in his career to take on the challenge of coaching his country.
"Becoming a national team coach is not something trivial. The federation made me understand that they wanted me 100 percent and that made it easy for me to choose," added the former Inter Milan, Manchester City, Galatasaray and Zenit St Petersburg coach.
"Being here in this role is important, and this was the right moment in my career."
Although Mancini and Balotelli had several run-ins when the pair were at Manchester City, he suggested the Nice forward would be given another chance.
"We'll talk, we'll probably call him. We want to see him play the way he did at the European Championship (in 2012)," he said.
Balotelli has not been called up for Italy since the last World Cup when his attitude was the subject of barely-veiled criticism from some senior players.
After scoring in the 2-1 win over England, Balotelli covered the entire Italy page in a Panini album with stickers of himself and then posted it on his Facebook page.
(Writing by Brian Homewood in Lyon, editing by Pritha Sarkar)
