ROME (Reuters) - The center-left candidate for Rome mayor in an election seen as a test of Italy's fragile coalition government was leading the field, projections showed on Monday, but the ballot is likely to go to a run-off next month.

Ignazio Marino of the Democratic Party (PD) would get between about 39 and 42 percent, according to the projections. His center-right rival, incumbent Gianni Alemanno of Silvio Berlusconi's center-right, would get between about 28 and 32 percent.

If the projections are confirmed by results, a run-off election will be held on June 9-10.

This will further drag out the race between the two sides, who are uncomfortable bedfellows in the right-left coalition government of Prime Minister Enrico Letta.

Letta's month-old government is struggling against slumping popularity, rising unemployment and the longest recession in Italy's post-war history.

A PD victory would give Letta a much-needed boost, while a failure by Marino to oust Alemanno could further fuel dissent among PD voters and factions in the party.

The PD was thrown into crisis by its failure to win February's national election outright and imploded last month in disagreement over the election of Italy's president.

The projections showed the candidate of the anti-establishment 5-Star Movement, which won 25 percent of the vote in its first national election in February, with about 13 percent and therefore excluded from a run-off.

Turnout figures showed a steep drop to 53 percent, down 20 points from previous mayoral elections in 2008.

While attention is on Rome, new mayors will be elected in 564 towns and cities involving 7 million voters.

(Reporting by Naomi O'Leary; Editing by Mark Heinrich)