The Eternal City has been run by emperors, barbarians, popes and dictators, but never by a woman.

That looks set to change in mayoral elections on Sunday with Virginia Raggi from the anti-establishment 5-Star Movement in pole position to wrest control of the capital from Prime Minister Matteo Renzi's centre-left Democratic Party (PD).

Defeat in Rome would be a blow for Renzi, but worse could be in store for him with his party also at risk of losing control of Italy's financial capital Milan in this weekend's run-off ballots, and facing difficult battles in Turin and Bologna.

Renzi has said the results will have no bearing on his government and has instead staked his political future on a referendum in October on plans to drastically curb the powers of the upper house or Senate.

However, a bad showing on Sunday will put him under intense pressure within a party already divided, and suggest he could find it hard to sell his reform package to the nation.

With the economy struggling to grow after years of austerity, Italians punished the PD in the first round of municipal voting on June 5. Renzi has not taken part in campaigning since then, a sign that PD candidates do not view him as an electoral asset.

"I cannot remember a party leader who has not been out on the campaign trail right at the death. It shows the difficulty he is in with this vote," said Piero Ignazi, professor of comparative politics at Bologna University.

EYES ON ROME

Sunday's vote takes in 126 towns and cities where no mayoral candidate won an outright victory two weeks ago, involving 8.6 million Italians - just under a fifth of the total electorate.

Most eyes will be on Rome, where 5-Star's Raggi, a 37-year-old lawyer, won a commanding 35.2 percent in the first round against 24.9 per cent for her nearest rival, the PD's Roberto Giachetti.

"The Romans are ready to turn a page and I am ready to govern this city and restore Rome to the splendour and beauty that it deserves," Raggi said ahead of Sunday's runoff.

Victory in Rome would give the 5-Star Movement, running second in national opinion polls, its biggest test at governing. If it proves itself in the capital, it will significantly boost its chances of winning the next parliamentary election, due in 2018.

But whoever takes charge in the capital faces a daunting task. The last mayor, from the PD, quit over an expenses scandal, dozens of city officials are on trial on Mafia-related charges and magistrates say the local administration is riddled with graft.

While a PD loss in Rome is widely seen as a foregone conclusion, the contest in Milan is much closer, and politically more significant for Renzi, who picked Giuseppe Sala, head of 2015's Expo World Fair in the city, as the PD candidate.

Sala won 41.7 percent of the vote against 40.8 percent for his opponent, Stefano Parisi, a relaxed, understated former city official who some political commentators believe could take charge of the fractured centre-right in the years ahead.

In nearby Turin, home of the carmaker Fiat and traditionally dominated by the left, the PD also faces an unexpectedly strong challenge from 5-Star. In another leftist bastion, Bologna, the PD is expected to hold off a centre-right candidate from the anti-immigrant Northern League party.

A loss in either of these cities would set alarms ringing in the PD and could encourage open revolt from party leftwingers who have accused Renzi of trying to drag the group towards the centre-right.

Italy's third-largest metropolis, the southern port city of Naples, is a lost cause for the party after Renzi's candidate failed to make it to the runoff, opening the way for a second term for outspoken former magistrate Luigi De Magistris.-Reuters