By James Mackenzie and Gavin Jones

ROME (Reuters) - Italian center-left leader Pier Luigi Bersani on Thursday appealed to all parties in parliament to back a new government, a move that may brighten prospects of resolving the political deadlock following last month's inconclusive election.

After meeting with President Giorgio Napolitano, Bersani said "all the forces in parliament" should support a government with a program of reforms presented by the center-left.

Asked if this meant he would also welcome the backing of Silvio Berlusconi's center-right, an option he has so far rejected, he said: "Yes, we are appealing to the whole of parliament to support the changes needed."

Bersani added, however, the center-right had so far rejected proposals by his Democratic Party (PD) on issues such as fighting corruption and legislation on conflicts of interest.

The election gave the alliance of Bersani's PD and the leftist SEL a majority in the lower house but not in the Senate, leaving it unable to govern without the support of other parties.

The stalemate has revived fears of a prolonged bout of instability in the euro zone's third-largest economy just as the crisis over bank deposits in Cyprus has raised concern of a fresh bout of financial market turmoil.

Napolitano completed two days of consultations on Thursday with political party chiefs and said he would announce his decision on the next step on Friday.

Bersani had previously tried to win support for a government from the anti-establishment 5-Star Movement (M5S) led by Beppe Grillo and shunned suggestions he might join forces with Berlusconi, as the PD did under outgoing technocrat Prime Minister Mario Monti.

Yet on Thursday, Bersani appeared to have lost patience with Grillo, who has repeatedly rebuffed him and who holds the balance of power in parliament.

"We have shown respect for the 5-Star movement's voters but they have shown no respect for ours," Bersani said.

After meeting the president on Thursday, Berlusconi repeated his demand that Bersani form a coalition with his conservative bloc and that Napolitano's successor as head of state should be from the center-right. Napolitano's term ends on May 15.

"There are two forces still in play, us and the Democratic Party, and at this moment the responsibility to give a government to the country lies with both of us," Berlusconi told reporters.

NEW ELECTION?

If no agreement can be struck, Italy faces the prospect of a brief period under a caretaker government before heading for a new election, possibly as early as June or after the summer.

With the country in deep recession and struggling with record unemployment and a 2-trillion-euro ($2.6 trillion) debt pile that remains vulnerable to the kind of financial market crisis that struck in 2011, business leaders and European partners are deeply concerned at the stalemate.

Bersani said on Thursday he will present a limited policy program focused on institutional reform, fighting corruption and creating jobs, and seek the backing of parliament.

Grillo's M5S on Thursday asked Napolitano for a mandate of its own, though it did not say who it would present as prime minister, and said it would not back any coalition, suggesting it will reject Bersani's call for unity.

"M5S will not give any confidence vote to political or pseudo-technocrat governments," Grillo said on his blog.

He rejected one option, widely mooted in Italian newspapers, that the newly elected speaker of the Senate, former anti-mafia judge Pietro Grasso, could be asked to lead a government.

Grasso is seen as a potential replacement for Bersani, whose position has been under threat ever since the election in which the center-left threw away a 10 point lead. He said on Thursday he was "ready to serve for the good of the country".

Napolitano has some room to appoint a technocrat prime minister from outside the main parties but any government would need the support of parliament.

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(Additional reporting by Naomi O'Leary, Roberto Landucci, Giuseppe Fonte; Editing by Sophie Hares)