Rome was the first city to declare its candidacy for the 2020 Olympics but then-Premier Mario Monti refused to provide government financial backing and the bid was dropped.
Letta first voiced support for a 2024 bid earlier this year.
Other potential 2024 bids could come from Paris; Doha, Qatar; and cities in the United States and Africa.
Speaking at the Italian Olympic Committee, Letta also discussed a law that will allow Serie A soccer clubs to break their leases with city-owned stadiums and build new venues that they own and operate privately.
Approving the stadium law could be a major boost toward reversing the recent decline of Serie A, which has been marked by falling attendance, fan violence and racism.
"This is the appeal that I will make to parliament that as of Jan. 1 there is a new law for modern venues," Letta said.
Letta was also meeting Wednesday with the committee working on a bid to bring the 2019 Alpine skiing world championships to Cortina d'Ampezzo. Cortina, which hosted the 1956 Winter Olympics, is competing against Are, Sweden.
Letta responded positively when Italian rugby federation president Alfredo Gavazzi asked if he would support a bid for the 2023 Rugby World Cup.
"Of course," Letta said. "And I want to inaugurate the World Cup as Premier."
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