The centre right is ahead in six of the provincial capitals after the first round two weeks ago – Massa, Pisa, Siena, Terni, Ancona and Brindisi – and behind in one, Vicenza.
In Sicily, there will be the first round of voting in 128 municipalities including big towns Trapani, Siracusa, Ragusa and Catania.
Before the vote Prime Minister Giorgia Meloni heavily targeted Catania, where rolling Rai news coverage of her election-eve rally brought a complaint for allegedly breaching equal time norms.
The centre left, on the other hand, is very keen to hold on to one of its longstanding fiefs, Ancona in Marche, which is also a regional capital.
In all, polling stations are open from 7am to 11pm Sunday and from 7am to 3pm Monday for the runoffs in 41 municipalities.
There are a total of 1,340,688 voters involved in the ballots.
Voting is also scheduled for the first round in 128 Sicilian municipalities.
The possible runoffs there are scheduled for Sunday, June 11 and Monday, June 12.
The same calendar is in place in Sardinia, where voters will go to the polls for the first round of municipal elections in 39 municipalities.
ANSA