Macron's victory over Eurosceptic Marine Le Pen in France's presidential election this month, gives "hope and faith in Europe", Gentiloni said at the Elysée presidential palace before the dinner.
But he agreed with the French president's campaign call for a Europe that is "stronger and closer to its citizens".
While Macron has called for a eurozone budget, finance minister and parliament, the Italian leader called for "fiscal and banking union".
"It's not an immediate prospect but it's important to begin working in that direction," he said.
Macron, who has already met German Chancellor Angela Merkel and European Council President Donald Tusk, called for a "real revival of our European perspectives", including a roadmap for a euro investment zone that would "reduce the differences between our economies".
He also noted the "challenges" that Italy faces in relation to migration, admitting that the rest of Europe did not react quickly enough to when it sounded the alarm on the question.
Heads of state of the G7 countries - the US, Japan, Germany, France, the UK, Italy and Canada - are to meet in Taormina, Sicily, on 26-27 May.
The French and German finance ministers, Bruno Le Maire and Wolfgang Schaeuble, were to meet in Berlin on Monday morning.