* President open to holding national elections a month early
* But says parliament must pass key legislation first
* Appears to offer compromise to parties on election date (Adds background, details, more quotes from statement)
By Philip Pullella
ROME, Nov 16 (Reuters) - Italy's president indicated on Friday that he was open to holding national elections on March 10 - a month earlier than foreseen - if parliament passes key legislation first.
Markets have been awaiting a signal on when the elections might be because of their desire that the next government continue economic reforms to overcome the debt crisis started by Prime Minister Mario Monti's year-old technocrat administration.
The elections in the euro zone's third-largest economy are due in spring after the end of parliament's five-year term and the date of the vote had been widely expected to be in early April, with April 7 the most touted date until now.
After meeting the speakers of parliament, President Giorgio Napolitano issued a statement saying he believed that elections for local governments in three Italian regions - Lazio, Molise and Lombardy - should be held on March 10.
But he also said Italians should be spared "a frantic succession of elections" if possible, indicating that the national vote could be held on the same date.
Angelino Alfano, the secretary of the centre-right People of Freedom Party (PDL), which has been calling for both elections to be held on one day, said he saw Napolitano's statement as a sign that national elections would be held on March 10.
Napolitano, who is the only person who can dissolve parliament and call early elections, said he wanted parliament to pass the 2013 budget before he makes his definitive decision.
The president also re-stated his hope that parliament could approve changes to Italy's convoluted election law before the end of the legislature.
The law, known as "the pigsty" because it is so messy, enables party leaders to handpick members of parliament and guarantees a strong majority to the winning coalition, however small their share of the vote.
There had been uncertainty over the date of the regional polls, particularly for Lombardy and Lazio, two regions where centre-right governments were driven out by corruption scandals.
The PDL - the party of former Prime Minister Silvio Berlusconi - fears it will do badly in both Lombardy and Lazio because of the scandals and some PDL leaders are concerned that could have a knock-on effect on the national vote if the two are held separately - and want both held on the same day.
Some in the party have suggested the PDL should withdraw support for Monti's government if the local polls were held first, bringing down the government and forcing an election before April.
By indicating he was open to national elections a mere month early under certain conditions, Napolitano appeared to be proposing a compromise between the centre right and centre left.
The PDL, which backs Monti in parliament under a cross-party agreement with the centre-left Democratic Party, is trailing in the opinion polls is not expected to form the next government.
Both the PDL and the PD will be holding primaries to choose their candidates for prime minister. The PDL is expected to choose its secretary, Alfano, and the PD is expected to choose its secretary, Pierluigi Bersani.
Berlusconi, who is on trial accused of paying for sex with a minor, has said he will not be a candidate.
Last month a Milan court convicted Berlusconi of tax fraud related to his Mediaset television company and handed down a four-year sentence that he will not have to serve until all appeals are exhausted. (Reporting by Philip Pullella and Naomi O'Leary; Editing by Robin Pomeroy)