* "Morally questionable" for Monti to run
* Election bid seen damaging Monti's independent status
* Opinion polls point to a centre-left victory
ROME, Dec 14 (Reuters) - Italy's main centre-left party, leading polls for next year's election, rebuffed calls for Prime Minister Mario Monti to run for a second term, a move one of the party's leading figures said would be "morally questionable".
The Democratic Party (PD) has supported Monti's technocrat government in parliament. But, while it has pledged to continue his fiscal discipline and wants him to stay on in some role after the election, it says he should stay out of the campaign, which polls suggest he would lose anyway.
"It would be illogical and in a certain sense morally questionable if the professor were to enter the race against the main political force which supported him in his reform efforts," Massimo D'Alema, a former prime minister and an influential centre-left elder statesman told Friday's daily Corriere della Sera. "I have great esteem for him and I hope he doesn't."
Centre-right candidate Silvio Berlusconi has offered to stand aside to allow a Monti candidacy.
European politicians from German Chancellor Angela Merkel to French President Francois Hollande also heaped praise on Monti and at a meeting of European centre-right parties on Thursday, he was urged by a number of politicians to run in the election.
Monti himself avoided commenting on his political future on Friday, telling a news conference in Brussels it would not be "either possible or appropriate" for him to speak on the matter.
Monti's austerity measures have helped lower borrowing costs since he took over in a financial crisis last year. Italy's public debt nonetheless rose above 2 trillion euros for the first time in October, according to the Bank of Italy on Friday.
PD party leader Pier Luigi Bersani said on Thursday he would call in Monti to perform some kind of role immediately after the election. But he has said it would be better for the respected former economics professor to stay out of the campaign.
If Monti does run, opinion polls suggest he would be defeated, and PD officials say it would then be much more difficult for him to be accepted as president to replace head of state Giorgio Napolitano, who must step down by April.
"Let's say that if he runs, it will be more complicated for him to become president of the republic because he would have been a political competitor not 10 years earlier or something like that but last week," Stefano Fassina, the PD's main spokesman on economic affairs told Reuters.
Napolitano, who named Monti to replace the discredited Berlusconi a year ago, said last month that Monti's special life-time seat in the Senate would not allow him to make an election bid.
Monti would also likely be cautious about any association with scandal-plagued Berlusconi, whose position switches have caused frustration and alarm across Europe and in his own party.
Berlusconi repeated criticisms of Monti's austerity on Friday and said he would be obliged to lead the centre-right if the former European commissioner did not take the role.
"I have had to return because of this," he told his own Italia Uno television station. "We're convinced that moderates will never allow the left to win with its policies of more spending and more taxes especially on the middle class."
A potential Monti election vehicle, a centrist group recently set up by Ferrari chairman Luca Cordero di Montezemolo, is polling under three percent in most surveys.
Analysts believe Monti would be unwise to run unless he has a good prospect of boosting this number to at least 15 percent.
An average of two weeks' opinion polls by website termometropolitico.it gave the PD 32.7 percent, ahead of the anti-establishment 5-Star Movement on 16.8 percent and Berlusconi's People of Freedom party (PDL) on 15 percent.
A potential centrist coalition that could back a Monti candidacy polled 9.2 percent.
Berlusconi's offer for Monti to campaign at the head of a centre-right made up of the warring PDL party and the separatist Northern League, which has been in opposition to the technocrat premier since the start, appears problematic.
The PDL precipitated Monti's decision to resign soon by withdrawing support for him in parliament last week.
The League noted Italy's debt has surged under Monti.
"There's record public debt under Monti, despite the ferocious increase in taxes. How can you support someone like that?" League leader Roberto Maroni tweeted on Friday.
Maroni has said the League would not enter an alliance with the PDL if Berlusconi is leader.