Local elections throughout Italy will be a major test for Matteo Renzi's government.

Local municipal elections take place throughout Italy on Sunday 5 June and again on 19 June in places where a run-off election is necessary if no candidate receives over 50 per cent of the vote in the first round.

Voting will take place in 1,342 cities and towns, 25 of which are provincial capitals and seven regional capitals. 13,316,379 people are eligible to vote, 6,382,798 men and 6.933,581 women. There are 18,318 first time voters and 46,781 European Union citizens who have registered to vote.

The polls are open on Sunday 5 and Sunday 19 June only, from 07.00 to 23.00, not on Monday as well. Voting is for mayors as well as local councils and municipalities in the larger cities.

The most important cities are Turin, Milan, Bologna, Rome and Naples, all of which are a test for the governing Partito Democratico (PD) and in particular for the government of prime minister Matteo Renzi.

In Turin, where there are 17 candidates, the incumbent PD mayor Piero Fassino looks as though he will be forced into a run-off with the Movimento 5 Stelle (M5S) candidate Chiara Appendino. If so it could be a close finish on 19 June.

Chiara Appendino

In Milan the PD's candidate Giuseppe Sala and commissioner of last year's successful Expo Milano 2015 is up against Stefano Parisi, the centre candidate supported by Silvio Berlusconi's Forza Italia and various other centre-right groupings. A run-off looks certain.

In Bologna the PD mayor Virginio Merola is standing for re-election and hoping to make it without a run-off on 19 June. Merola is no fan of the prime minister and his victory could be more to do with the fractious fighting to her political right and the disarray in the M5S than a positive vote for Renzi's PD.

The election in Rome, where there are five candidates is crucial for Renzi. Roughly from left to right on the political spectrum are Stefano Fassina (Sinistra Italiana), Roberto Giachetti (PD), Virginia Raggi (M5S) whose policies sometimes sound left and other times right, Alfio Marchini (Forza d'Italia and other groupings) and Giorgia Meloni (Fratelli d'Italia and Lega Nord). Having forced out the previous PD mayor, Ignazio Marino, last autumn, Renzi has put all his weight behind Giachetti, his personal choice for candidate. Giachetti won't manage a clean victory on 5 June and may not even come out in first place, which could go to Raggi. The likely run-off scenario on 19 June is Giachetti and Raggi. Should Raggi win – or should Giachetti not even make it to the run-off – it would be a serious defeat for Renzi.

Virginia Raggi

In Naples, the one-time mayor Luigi de Magistris (supported by a civic list and the left-wing Sinistra Ecologia Libertà (Sel) is trying to make a come-back. He is against three other main candidates – Gianni Lettieri, supported by Forza Italia, Valeria Valente (PD) and Matteo Brambilla M5S. De Magistris is ahead, trailed by Lettieri but it is unlikely he will win on the first round. At present it looks as though Lettieri will make it into the run-off but a last minute spurt could push the PD's Valeria Valente into the second round of voting on 19 June.

Valeria Valente

If the PD were to lose Milan and Rome it would be serious news for the party. If the PD also failed to clinch Turin it would be a real danger signal for Prime Minister Renzi however hard he tries to convince voters that these local elections are not a test of his political standing. And if Appendino were to win in Turin and Raggi in Rome, two of Italy's most important cities, the M5S would be jubilant.