By Steve Scherer and Naomi O'Leary

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 from 41 to 43 percent of the vote while his center-right rival, incumbent Gianni Alemanno of Silvio Berlusconi's center-right People of Freedom (PDL) party, was set to take 28-30 percent.

The rival parties are uncomfortable bedfellows in the right-left coalition government of Prime Minister Enrico Letta, whose month-old government is struggling against slumping popularity and the longest recession in Italy's post-war history.

Beppe Grillo's anti-establishment 5-Star Movement, which stormed into parliament by winning a quarter of the national vote in February, was on track to win less than 13 percent in Rome, half its result just three months ago.

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

"The left is claiming victory, but the run-off is a whole new game, and it's wide open," Alemanno told a news conference. Marino said: "The vote shows the need and desire for change."

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

The PD was thrown into crisis by its failure to win the national election outright after polls showed it leading strongly a month beforehand. After the vote, then-PD leader Pier Luigi Bersani sought the support of Grillo to form a government but was rebuffed, forcing him to turn to Berlusconi's bloc.

"The 5-Star Movement and Beppe Grillo lost their big chance for change," Bersani spokesman Stefano Di Traglia tweeted in reference to the movement's poor showing in Rome. "Who knows if it will come around again?"

But local votes are often more closely tied to the charisma and appeal of individual candidates, and opinions about the performance of the incumbent, than to the sweeping issues that dominate national elections.

Alemanno's administration was harshly criticized for cronyism, especially at the municipal transport company, and for generally being ineffective, as happened when 5 inches of snow brought the city to a standstill for several days last year.

Marino is a well-known figure in the PD, a surgeon by profession who spent many years working in the United States.

Turnout figures showed a steep drop to 53 percent, down more than 20 percent from the previous mayoral election in 2008.

While most attention was on Rome because it was by far the biggest city holding an election, new mayors were voted on in 564 towns and cities involving 7 million voters.

(Additional reporting by Roberto Landucci; editing by Mark Heinrich)