Italy's eurosceptic and anti-establishment opposition party, the Five Star Movement (M5S), made strong gains in a first round of nationwide local elections, while Prime Minister Matteo Renzi's Democrats (PD) suffered setbacks, results showed Monday.

About 13 million people - a quarter of the electorate - were called to elect new mayors in more than 1,300 municipalities. But the most important race in the Sunday vote was in Rome, where the M5S fielded 37-year-old lawyer Virginia Raggi.

With 98 per cent of the votes counted, she led the race at 35.3 per cent, while PD candidate Roberto Giachetti was trailing at 24.8 per cent. Since the 50-per-cent victory threshold was not cleared, a run-off between the top two finishers is due on June 16.

"Ladies and gentlemen, the wind is changing, the wind is changing," Raggi said in overnight comments. "This is only the half time result, there will be a final sprint, but it is a historic moment," she added.

"I think that in these local elections, Italians have recognized that we are fit for government," Luigi Di Maio, seen as an M5S prime ministerial candidate in general elections due within two years, said on the party's website.

Barring a major upset, Raggi is poised to become Rome's first-ever female mayor and the youngest in at least a century. That would save the M5S leader, comedian Beppe Grillo, from making good on a campaign promise to "set [him]self on fire" in case she did not make it.

Raggi presented herself as a clean broom in a city with broken public services and crippling debt, rattled by a major corruption scandal involving previous administrations which partly contributed to the downfall of outgoing PD mayor Ignazio Marino.

The election outcome suggested that Renzi - battling with banking crises, a stagnant economy and surging migration - is experiencing a midterm slump in popularity, complicating campaigning for another key vote scheduled for October.

Italians are set to vote in a referendum on a major constitutional reform that would emasculate parliament and strengthen central government. Renzi has staked his career on a 'yes' victory, pledging to otherwise quit politics.

The premier said he was "not happy" about Sunday's elections, but insisted that they were a mixed bag for all major parties.

"There are chequered results for the right, chequered results for the Five Star [Movement], chequered results for the PD," he said in a press conference. "I don't believe there is a correlation between the referendum and the local elections," he added.

The Rome result risked to be even more embarassing for Renzi, as preliminary counts at one time pointed to an all-female run-off between Raggi and far-right leader Giorgia Meloni, who eventually slid into third place behind Giachetti.

PD candidates had a tough time in other key races: in Turin and Bologna incumbent mayors started out as frontrunners, but were forced into run-offs with conservative or M5S opponents that could produce surprising results in two weeks' time.

In Milan, the Democrats had high hopes on Giuseppe Sala, who oversaw the city's successful Expo world fair last year. He drew almost level at about 41 per cent with conservative Stefano Parisi, whose good score reflected well on his chief sponsor Silvio Berlusconi.

The former premier's strategy worked less well in Rome, where his centre-right camp failed to unite around one candidate. Had it done so, it would have outperformed the PD and stood a chance of beating Raggi in the second round.

As for the M5S, its success in Rome was tempered by less-than-stellar performances in Naples and Milan, where it won only about 10 per cent of the votes, and by the fact that it ran in only about a fifth of municipalities that held elections.

With voting taking place at the end of a bank holiday weekend, a low turnout was widely expected. Only 62.1 per cent of eligible voters cast their ballots, compared to 67.4 per cent in the previous elections, the Interior Ministry said.

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