ROME, Sept 30 (Reuters) - Mayoral elections in Italy"s largest cities on Sunday and Monday are expected to illustrate Matteo Salvini"s weakening grip of the right and see centre-left wins in the most high-profile contests. A parliamentary by-election in the Tuscan city of Siena will also be closely watched because it holds the key to the future of Democratic Party (PD) leader Enrico Letta, who is one of the candidates. Some 12 million voters will be eligible to elect mayors of Rome, Milan, Naples and Turin and more than 1,000 smaller centres, in the first test of voter sentiment since Mario Draghi became prime minister in February. Salvini, who seemed on an unstoppable rise when he led his League party to a triumph at European elections in 2019, has seen his popularity slide and his party risks being overtaken by its hard-right ally Brothers of Italy. "These mayoral elections will test the balance of power on the right, but I"d be cautious about drawing conclusions from them for the national picture," said Lorenzo Pregliasco, head of polling and political analysis firm YouTrend. Salvini is facing growing internal opposition from more centrist League politicians, and he suffered a major blow this week when one his closest aides resigned after being embroiled in a drugs scandal. read more The League has seen its support slide from the 34% it won at the European vote to around 20%, according to recent polls. It is now roughly level with Brothers of Italy and the PD. The League and the PD are both in Draghi"s national unity government, along with the 5-Star Movement which is polling at around 16%, while Brothers of Italy is in opposition. The rightist alliance, which includes Silvio Berlusconi"s Forza Italia, leads nationally but its support is strongest in small towns and villages, and its candidates are expected to lose out in most of the main cities up for grabs. Opinion polls published before a black-out was imposed two weeks before the vote pointed to centre-left victories in Rome, Milan and Naples, while Turin looks harder to call. Where no candidate reaches 50% of the vote in the first round on Sunday and Monday, a run-off between the first two will be held two weeks later. In the capital, former Economy Minister Roberto Gualtieri from the PD is expected to oust 5-Star"s incumbent Virginia Raggi, but a run-off will almost certainly be needed. That is likely to be between Gualtieri and the right"s candidate Enrico Michetti, a local lawyer and radio journalist, with Raggi seen limping in third. Milan"s centre-left incumbent mayor Giuseppe Sala looks headed for re-election, possibly without the need for a run off. In the Siena by-election PD leader Letta, who in March gave up an academic career in Paris to head up the party, is seeking a seat in parliament and has raised the stakes by saying he will quit as party leader if he loses. He is expected to prevail in what is a traditional PD stronghold, but YouTrend"s Pregliasco cautioned that the outcome should not be taken for granted. "The turnout at these by-elections is normally very low, but rightist voters could be motivated by the chance to kick Letta out of the PD leadership," he said.