By James Mackenzie

ROME (Reuters) - Italy's battered center-left won the election for mayor of Rome and 15 other major cities on Monday, giving a lift to Prime Minister Enrico Letta as he strives to control an uneasy coalition with traditional rivals on the right.

The center-left candidate in Rome, former surgeon Ignazio Marino, took 64 percent of votes in a run-off ballot on Sunday and Monday, defeating the outgoing mayor Gianni Alemanno, who won 36 percent, the Interior Ministry said.

"Today is a day that the center-left has won extraordinary results in many cities across Italy," Marino told reporters. "This is the capital and we need to regain the role of moral leader for our country," he said.

With around 6 million Italians eligible to vote in more than 500 towns and cities, the elections were the first big test since the formation of the Letta government in April, which came after a prolonged stalemate caused by an inconclusive national poll in February.

The grand coalition between Letta's center-left Democratic Party (PD) and Silvio Berlusconi's center-right People of Freedom (PDL) party has aroused little enthusiasm, even among its members, but it was the only viable possibility after no party secured a majority in parliament.

Monday's result underlined broad popular disillusionment with Italy's parties, with a dramatic slump in voter turnout in the capital to 45 percent, down from 63 percent in the run-off in 2008 when Alemanno became mayor.

Despite the poor turnout, the vote offers a welcome success for the badly divided PD, which nearly imploded after throwing away the 10-point lead it held ahead of the national election.

"On the whole, the (election) result strengthens the grand coalition government," Letta commented. "I'm convinced that today we are capable of doing good work to obtain the results that citizens expect."

The left won all 16 provincial capitals in the race, including Rome, to regain some momentum after its disastrous start to the year, which saw Pier Luigi Bersani toppled as party leader.

By contrast, Berlusconi's PDL and the anti-establishment 5-Star Movement of comic Beppe Grillo - the two main beneficiaries of the PD's collapse in February - were left licking their wounds after failing to score any notable successes.

PDL, 5-STAR MOVEMENT LOSES OUT

Grillo's party, which rode a wave of popular discontent to take almost a quarter of the national vote in February, saw almost all its candidates eliminated in the first round two weeks ago. It won only two towns.

It faces an even more telling test in Sicily, where a separate set of local balloting was held on Sunday and Monday. Sicily was the scene of one of its greatest triumphs last year and a springboard for its national success.

The movement has been shaken by growing concern about Grillo's authoritarian style and his attempts to impose iron party discipline on parliamentarians. Last week two lawmakers left the group, complaining about control over decision-making.

The local elections have no direct impact on national government but the result should reinforce the position of Letta, who has had to struggle with widespread perceptions that Berlusconi is pulling the strings in the coalition.

Although Berlusconi is not a member of the government, the 76-year-old media billionaire has pressed the prime minister for aggressive tax cuts, despite the strained state of Italy's public finances, saying they are a condition for his support.

Berlusconi took little part in the campaign and officials from his center-right People of Freedom (PDL) acknowledged the party suffered badly as a result.

"At national level, the party is still being pulled up by Berlusconi and that's shown in the opinion polls. That effect doesn't work at local level because we've been slow to build a truly democratic party," said Fabrizio Cicchito, a senior PDL lawmaker.

Letta has pledged measures to lift the economy out of its two-year recession and cut dramatic levels of youth unemployment as well as reforming a sclerotic political system that has repeatedly allowed special interest groups to block reform.

But he faces an uphill struggle with the economy set to contract by 1.3 percent this year according to government forecasts.

Official data on Monday showed the economy shrank by 0.6 percent in the first quarter of this year and industrial output was weaker than expected in April, falling for a third month running and offering no hope that the slump will end soon.

(Additional reporting by Steve Scherer, Antonio Denti, Gavin Jones and Catherine Hornby; Editing by Andrew Heavens)