Twenty million voters are to elect governors in seven of the country's 20 regions, as well as the mayors of more than 1,000 municipalities.
This polling battle is the first in Italy, which is slowly emerging from recession, since European elections a year ago in which Renzi's centre-left Democratic party (PD) won with just over 40 per cent of the vote.
Observers will also be looking closely at the battle on the right between the anti-immigration Northern League, led by rising star Matteo Salvini, and Forza Italia (Go Italy), the party of former prime minister Berlusconi.
At present, five of the seven regions holding elections are governed by the left, one is led by the League and another by Forza Italia.
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In Campania in the south, the PD's candidate Vincenzo De Luca, fighting the Forza Italia incumbent, has been named in a list of 17 "unpresentable" candidates by an anti-mafia commission.
De Luca has a conviction for abuse of power and faces trial on other charges, including fraud, and could be banned from taking office.
"The alternatives to Renzi are not very attractive, he remains the only serious political offer," said Giovanni Orsina, political scientist at the Luiss University in Rome.
The betting odds suggest a score of 6-1 to the Italian left, with wide expectations that Veneto in the northeast will remain with the League, or 5-2 or even 4-3.
"4-3 for us football fans evokes fond memories," said Renzi recently, referring to the result of the semi-final of the 1970 World Cup won by Italy against West Germany.