* Parliament holds new ballot, no deal in sight
* Parties fail to put forward candidate
* Lawmakers pushing for new mandate for outgoing president
* Push for woman president hits resistance
By Crispian Balmer and Giuseppe Fonte
ROME, Jan 29 (Reuters) - Italy's parliament voted for a sixth day running on Saturday to elect a new president, but the parties remained deeply divided over a possible candidate, with the leaders struggling to control their own lawmakers.
The week-long search to find a replacement for Sergio Mattarella, whose seven-year mandate expires on Feb. 3, has laid bare the fragility of Italian politics and highlighted a failure of leadership in the main centre-right and centre-left blocs.
"Seeking a name in the chaos," top-selling daily Corriere della Sera said on its front page headline. "More vetoes than votes," Catholic daily L'Avvenire wrote.
The heads of both the rightist League party and 5-Star Movement, which is allied to the centre-left, said late Friday they wanted a woman to become president for the first time and indicated that a deal was at hand.
Political sources said both groups were backing Elisabetta Belloni, who heads the secret services, but the news provoked a sharp backlash from other parties, splintering the centre-right bloc and sowing dissent in 5-Star ranks.
The president is a powerful figure in Italy, who gets to appoint prime ministers and is often called on to resolve political crises in the euro zone's third-largest economy, where governments survive barely a year on average.
Unlike in the United States or France, where heads of state get elected in a popular vote, in Italy, 1,009 parliamentarians and regional representatives chose the winner in a secret ballot https://www.reuters.com/world/europe/italian-presidential-elections-shrouded-parliamentary-secrecy-2022-01-13, which party leaders sometimes struggle to control.
Threatening to ignore their leaders and take charge of the situation themselves, lawmakers have been increasingly voting for Mattarella in the ballots, despite the fact that he himself has ruled out a second mandate.
In Friday's second vote, he received 336 ballots, up from 160 on Thursday and 125 on Wednesday. "Parliament wants Mattarella," La Repubblica daily said in a frontpage headline.
It remains far from clear whether Mattarella, 80, would accept another term, but many lawmakers believe his reappointment is the best way to maintain the status quo and enable the government to re-focus on battling the COVID-19 pandemic.
The repeated failure to find any sort of consensus has poisoned the political atmosphere, with potentially dangerous consequences for the stability of the broad coalition backing Prime Minister Mario Draghi's government.
Draghi himself has made clear he would like the job of president, but the main parties have so far refused to put his name to a vote, partly out of fears that the abrupt switch of roles could cause the fragile government to implode.
As voting resumed on Saturday, no party orders had filtered down on which way lawmakers should vote, with the various blocs apparently in disarray.
5-Star chief Giuseppe Conte did not show up at a meeting of centre-left leaders while the centre-right Forza Italia party said it would no longer seek a solution in partnership with its traditional allies the League and Brothers of Italy.
(Additional reporting by Angelo Angelo Writing by Crispian Balmer Editing by Frances Kerry)