Italy's anti-establishment 5-Star Movement took a large lead in the first round of voting for the mayor of Rome, according to early results on Sunday, in a possible blow to Prime Minister Matteo Renzi.

Some 13 million people, or a quarter of the adult population, were eligible to vote for mayors in around 1,300 towns and cities, with attention focused firmly on a handful of major centers, including the capital.

Victory in Rome would be a huge breakthrough for 5-Star, which was founded in 2009 by comedian Beppe Grillo and hopes to capitalize on anger over corruption scandals that have embroiled both left-wing and right-wing parties in the city.

The 5-Star candidate in Rome, Virginia Raggi, was likely to win 36.7 percent of the vote, according to a projection by Piepoli Institute based on a partial vote count.

Roberto Giachetti, from Renzi's center-left Democratic Party (PD), was projected at 23.1 percent, marginally ahead of far-right candidate Giorgia Meloni, on 22.2 percent.

If no one wins more than 50 percent in the first round, runoffs between the top two candidates will be held on June 19.

It would be a major setback for Renzi if his candidate fails to reach the runoff in the capital, where the previous mayor was from the PD and was forced out in disgrace in October following a scandal over his dining expenses.

A victory for Raggi would make her Rome's first woman mayor.

The race looked closer in Italy's financial capital, Milan, where a first projection had center-left candidate Giuseppe Sala ahead with 42.8 percent, followed by the center-right's Stefano Parisi with 37.7 percent.

Renzi, whose popularity has sagged over the last year, has distanced himself from the mayoral elections, arguing that they reflected local issues and would have no repercussions for his coalition government.

Instead he has tried to focus attention on a referendum in October on an overhaul of the constitution, saying he will resign if Italians reject his plan to reduce the powers of the Senate and streamline lawmaking procedures in Parliament.

In the other main cities, projections suggested that in Turin the incumbent center-left mayor Piero Fassino was ahead, but was likely to face an unexpectedly tough runoff against a 5-Star candidate.

Naples looked set to be held by leftist incumbent Luigi de Magistris, an independent former prosecutor who has declared the city a "Renzi-free zone." A runoff is projected against the center-right candidate who was seen in second place.

In Bologna, a traditional center-left stronghold, the PD-backed candidate was ahead but by less than expected and looked likely to face a runoff against either 5-Star or the right-wing Northern League.