He also said he saw Rome as the frontrunner in the race to host the 2024 Games.
"To those of you who want to win gold medal number 200, I say there isn't much time," he joked with Azzurri athletes at the ceremony.
"We're back in Italy on Sunday".
Renzi, who opened Italy's Casa Italia base in Rio on Wednesday, will watch some events on Saturday after taking part in the Olympics opening ceremony on Friday.
Italy has won 199 gold medals so far in Olympic history.
"I don't want to put pressure on the athletes," Renzi added.
"I'll be at the shooting, at (Rossella) Fiammingo's épée fencing contest, at (Gabriele) Detti's 400 metres freestyle".
ANSA