* Local polls come ahead of national vote due by May 2018
* Center-right performed strongly in June 11 first round
* Anti-establishment 5-Star still strong at national level (Adds start to voting, early turnout, government still working on banks decree)
ROME, June 25 (Reuters) - People in more than 100 Italian towns and cities voted on Sunday to pick municipal mayors in a run-off ballot that could bolster center-right parties ahead of a national election due in less than a year.
The vote could be a test of the current political mood in Italy, where a gradual economic recovery has not yet improved most Italians' living standards or significantly cut unemployment.
Anti-European sentiment has increased in the country in the past few years, fueled by EU-imposed austerity policies and the waves of migrants arriving from north Africa which Rome feels it is being left alone to cope with.
The center-left government is also under pressure to tackle its latest banking crisis, scrambling to put together an emergency decree to wind down two Veneto-based regional lenders before bank branches and markets reopen on Monday.
In Sunday's ballot, about 4.3 million voters are expected to go to the polls in municipalities that are still up for grabs because no candidate won more than 50 percent of votes in the June 11 first-round election.
Center-right candidates backed by the anti-immigrant Northern League and Silvio Berlusconi's Forza Italia party won a strong showing in the first round, and were ahead in 13 of the 22 provincial capitals going to a run-off.
Center-left candidates backed by the ruling Democratic Party (PD) were ahead in six, while in three cities the leading candidate is an independent supported by neither side. Early turnout was low at 14.9 percent by midday (1000 GMT), down from 19 percent at the same time two weeks ago.
Italy's national parliamentary election must be held by May 2018 but the broad coalition backing Prime Minister Paolo Gentiloni is fragile and political analysts say an early vote this autumn cannot be ruled out.
Although Sunday's vote will be one of the last before the general election, local factors mean it may not provide a clear reflection of parties' national popularity.
In the first round, the anti-establishment 5-Star Movement only reached the run-off in one of the main 25 towns and cities but is Italy's most popular party at a national level, according to many opinion polls.
Nevertheless, Sunday's result could serve as a call to unify among the center-right parties, which are in competition at the national level.
Their strong first-round showing suggests that if the parties can unite under a single leader they would be a force to be reckoned with at the general election.
Sunday's most closely watched contest will take place in the northern port of Genoa, a traditionally left-wing stronghold that could fall to the center-right for the first time in 50 years, with a candidate backed by the Northern League ahead after the first round.
That would be a setback for PD leader and former Prime Minister Matteo Renzi, who has taken a back seat in campaigning for the mayoral elections after seeing his party roiled by internal divisions this year.
In other important cities, the center-right leads in Verona and Padua in the north while the center-left is ahead in L'Aquila, the capital of the central region of Abruzzo.
In the northern city of Parma, 5-Star's first ever mayor, elected in 2012, is running as an independent after falling out with the party leadership, and leads against a center-left rival going into the run-off.
Exit polls will be published for six of the main cities when polls close at 11 pm. (2100 GMT) and first projections based on the actual vote count will be released about 45 minutes later. (Reporting by Gavin Jones; Editing by Helen Popper and Jane Merriman)