The 89-year old had announced in December that he would be leaving office well before the end of his term in 2020 because of his advancing age.
He had been persuaded in 2013 to stay on for an unprecedented second term after deadlocked elections sparked a political crisis in the eurozone's third-largest economy -- but had always been expected to step down early.
Prime Minister Renzi paid tribute to the president yesterday, telling the European Parliament that Napolitano had been a man driven by the desire to reform, who "faced moments of great difficulty with intelligence and wisdom."
Potential candidates for the new head of state include former prime ministers Romano Prodi and Giuliano Amato, as well as Economy Minister Pier Carlo Padoan, Defence Minister Roberta Pinotti and former Rome mayor Walter Veltroni.
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European Central Bank chief Mario Draghi on Wednesday rejected speculation that he had his eye on the job.
"The election of the President of the Republic, just like the election of the pope, is completely unpredictable, but unlike a conclave (papal election), it doesn't even have the help of the Holy Spirit," said Luigi La Spina, editorialist for La Stampa daily.
"Napolitano has been president in one of the most difficult phases in our country, not just politically but economically," Francesco Clementi, professor of constitutional law at the Luiss University in Rome, told AFP.
"I think the presidential election will certainly be complex...The government will have to work hard" to find a figure who will suit parties from across the political spectrum, he said.
The election does carry political risks for Renzi, whose government was ushered into power last year with Napolitano's blessing.
The 40-year old will want a candidate who can help bridge political differences which otherwise threaten to scupper the PM's ambitious reform programme.