By Catherine Hornby

ROME (Reuters) - Italy's battered center-left won the election for mayor of Rome on Monday and appeared set to do well in other cities, 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, former surgeon Ignazio Marino, took 63.8 percent of votes in a run-off ballot on Sunday and Monday, defeating the outgoing mayor Gianni Alemanno who won 36.2 percent, a partial Interior Ministry count showed.

"The fact is that Marino has won, we have to accept that," said Andrea Augello, a close aide of Alemanno.

With about six million Italians eligible to vote, the elections were the first major test of sentiment since the formation of the Letta government in April.

However, popular disillusionment with Italy's parties was evident from the dramatic slump in voter turnout in the capital to an all-time low of 45 percent, down from 63 percent in the run-off in 2008 when Alemanno became mayor.

Despite the poor turnout, the result offers a welcome success for Letta's center-left Democratic Party (PD), which nearly imploded after throwing away a 10-point lead it held ahead of Italy's inconclusive general election in February.

The party then upset more voters by forming a government with center-right adversary Silvio Berlusconi and Letta has struggled to convince many Italians that he is truly leading the administration and not the charismatic media mogul.

Preliminary results on Monday showed some signs of voter confidence in the center-left elsewhere too. It was well ahead in the cities of Ancona, Viterbo and Treviso and was on track to win in every provincial capital in the race.

In Siena, a traditional stronghold of the left, voting was neck-and-neck after a scandal at the Monte dei Paschi di Siena bank tarnished the image of the center-left city government.

The anti-establishment 5-Star Movement of comic Beppe Grillo, which rode a wave of popular discontent to take almost a quarter of the national vote in February, fared badly in the elections, with almost all of its candidates eliminated in the first round two weeks ago.

The movement 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. Last week two lawmakers abandoned the group, complaining about his control over decision-making.

BICKERING

The low turnout reflected widespread discontent with corruption, waste and mismanagement at national and city levels.

While good news for Letta, the result was a blow to the center-right and could weaken some of Berlusconi's more combative lieutenants who have been pressing the prime minister to make aggressive tax cuts.

With constant internal bickering, the left-right coalition government's popularity has dropped and few Italians have confidence that it can end economic stagnation or reform the country's sclerotic and inefficient institutions.

Letta has had to reconcile competing demands for tax cuts and job-creating measures to pull Italy out of recession with pledges to shore up public finances and cut state debt.

Official data on Monday showed Italy's economy contracted 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.

(Editing by Gareth Jones)