ROME (Reuters) - Italians vote on Sunday for mayors of their largest cities in a ballot that will test Prime Minister Matteo Renzi's popularity and could hand control of the capital Rome to the anti-establishment 5-Star Movement (M5S).

Renzi's Democratic Party (PD) took a bruising in the first round of voting on June 5. Italy's four biggest cities are among 126 towns holding run-offs between first and second-placed candidates after none won more than 50 percent backing.

Attention will focus on Rome, the financial hub Milan and the traditional PD stronghold Turin as 8.6 million people - just under a fifth of the total electorate - cast their vote.

Rome looks set to pass from PD rule to elect Virginia Raggi of M5S, who won 35.2 percent in the first round and pushed Renzi's candidate into second place with a campaign promising to fight graft and privilege.

Renzi has said the vote will not hurt his left-right coalition government, but a bad showing will put him under pressure in his already divided party ahead of a referendum in October on which he has staked his political future.

The most politically significant contest for Renzi is in Milan, where he backed Giuseppe Sala, head of the 2015 Expo World Fair. Sala emerged from the first round barely a percentage point ahead of center-right rival Stefano Parisi.

In Turin, prominent PD incumbent Piero Fassino came out ahead in the first round but faces an unexpectedly tough challenge from M5S. In Bologna, another leftist bastion, the PD is expected to hold off the anti-immigrant Northern League.

Naples is a lost cause for the PD, whose candidate was knocked out in the first round. Italy's third-biggest city looks set to give a second term to former prosecutor Luigi de Magistris, who has declared it a "Renzi-free zone".

Voting opens at 7 a.m. (0100 EST) and closes at 11 p.m., when the result of exit polls will be announced for the main cities. Initial projections based on the vote count will be issued after about an hour, and then at regular intervals.

(Reporting by Isla Binnie; Editing by Tom Heneghan)