The focus is on the major cities of Bologna, Milan, Naples, Turin and especially the capital Rome, where the populist anti-establishment Five Star is heading the race for the mayor's seat.
Despite the possibility his centre-left Democratic Party (PD) could lose control of both Rome and Milan, Renzi has played down the significance of the vote.
On Sunday, as if to demonstrate his insouciance, the 41-year-old prime minister visited the training camp of the Italian football squad, to wish them luck in the Euro 2016 championships starting in France next week.
Rome has been without an elected leader since last October, when Ignazio Marino, a member of Renzi's PD, was forced to quit over an expenses scandal.
Voting in the Trastevere district of the capital, Rolando Antonucci, 78, told AFPTV he hoped for greater civic-mindedness "among citizens and lawmakers alike".
"I came to vote because I have hope... Who knows, maybe for once I will be satisfied with my vote."
Nationwide, more than 13 million people were eligible Sunday to choose members of 1,300 municipal councils in a two-round ballot to be completed on June 19.
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