* Bersani, Berlusconi agree on Marini as president
* Bersani faces revolt over "last-century candidate"
* 5-Star Movement proposes academic favoured by many on left
By James Mackenzie
ROME, April 18 (Reuters) - Italy's divided parliament begins voting for a new state president on Thursday, with former Senate Speaker Franco Marini the main candidate in a ballot that will severely strain the unity of the centre-left alliance led by Pier Luigi Bersani.
The vote for a successor to President Giorgio Napolitano, whose term ends on May 15, will be a crucial step towards resolving the stalemate since the inconclusive election in February left no party with enough support to form a government.
Even by the tangled standards of Italian politics the situation is complicated, but until the new president is elected, the paralysis that has hobbled government more than 50 days after the election will continue.
Marini, a prominent Catholic and former head of the moderate CISL union, was chosen after a concerted effort by Bersani to get an accord with centre-right leader Silvio Berlusconi and the small centrist grouping of caretaker Prime Minister Mario Monti.
But Bersani's decision to propose a candidate with little public backing who lost his seat in parliament in the last election sparked fury in the ranks of his own party, many of whom suspected a deal with Berlusconi.
"Voting for Franco Marini today would be to do a disservice to the country," Matteo Renzi, the 38-year-old mayor of Florence who is Bersani's main rival for leadership of the centre-left, told La7 television.
He described the 80-year-old former unionist as "a candidate from the last century" who had no charisma or international standing. Renzi said it was unacceptable that his candidacy was based largely on the fact he was a well-known Catholic.
He said his supporters in parliament, thought to number more than 50, would not vote for Marini, and dozens of others on the centre-left were also reported to be prepared to defy Bersani, leaving the result of Thursday's vote uncertain.
On Wednesday, the anti-establishment 5-Star Movement led by former comic Beppe Grillo named its candidate as Stefano Rodota, a left-wing politician and academic who is anathema to Berlusconi but who many in the centre-left would be prepared to support.
February's election gave Bersani's centre-left alliance control of the lower house of parliament but short of the Senate majority it needed to form a government and unable to agree to a deal with either Grillo or Berlusconi.
The 61-year-old former industry minister has faced growing pressure from Renzi and others in his party after throwing away a 10-point opinion poll lead before the vote.
While the fiery Grillo remains firmly opposed to the main parties, agreement over the candidacy of Marini could signal greater willingness on the part of Bersani and Berlusconi to come to an understanding to avert immediate new elections.
The head of state is a largely ceremonial figure but has a number of vital political functions, as Napolitano demonstrated in 2011 when he put Mario Monti at the head of a technocrat government to replace the scandal-plagued Berlusconi.
It will be up to the new president to end the political deadlock left by the election, either by persuading the parties to come to an accord that would allow a government to be formed or by dissolving parliament and calling a new national vote.
A joint sitting of the two houses of parliament, joined by 58 regional delegates, will begin voting on Thursday at 10 a.m. (0800 GMT), but no result may be reached before the weekend if Marini does not secure sufficient backing.
Two rounds of voting will be held every day, with a two-thirds majority or 672 of the 1,007 electors needed in the first three rounds.
If no candidate succeeds in the initial rounds, the required threshold drops to a simple majority in subsequent rounds. But it is unclear whether Marini would remain in the race or drop out if he failed to secure the two-thirds majority.
Before Marini's name was announced on Wednesday evening, favourites had included former Prime Ministers Giuliano Amato, Romano Prodi and Massimo D'Alema as well as constitutional court judge Sabino Cassese.