By Catherine Hornby

ROME (Reuters) - Italian local elections that end on Monday could give a morale boost to Prime Minister Enrico Letta and confirm that support for the populist 5-Star Movement is waning.

Despite a slump in turnout as Italians lose faith in their politicians, Letta hopes for a positive result for his center-left Democratic Party (PD), which nearly imploded after throwing away a 10-point lead it held ahead of February's inconclusive general election.

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.

In Rome, the PD's Ignazio Marino took a strong lead over center-right Mayor Gianni Alemanno in a first-round vote at the end of May, raising the chances that Letta's party will win back control of the capital city.

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, looked set to fare badly after its support fell sharply in the first round.

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.

ECONOMIC GLOOM

By the end of the first day of voting on Sunday, turnout stood at only 34 percent, down from about 42 percent at the same stage in the first round, in which there was an overall turnout of about 62 percent. Some 75 percent of eligible Italians voted in February.

Voting resumed at 7 a.m. (0500 GMT) and will close at 3 p.m. (1300 GMT), with results expected by the evening.

In Rome, turnout slumped to 32 percent from 38 percent at the same stage in the first round, in which only about one in two eligible voters bothered to cast a ballot.

With constant internal bickering, the left-right coalition government's popularity has dropped and few Italians have confidence it can pull the economy out of stagnation.

Letta has had to reconcile competing demands for tax cuts and job-creating measures to get Italy out of nearly two years 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, offering no hope that the slump will end soon.

Some 6 million Italians are eligible to vote in local elections in cities including Rome, Siena, Ancona, Brescia and Viterbo and several towns across Sicily.

(Editing by Robin Pomeroy)