* Draghi trying to muster party support to form government
* Previous govt collapsed after coalition rupture
* Draghi has potential backing of most parties
* To hold more talks next week(Recasts, changes slug, adds quotes, background)
By Gavin Jones and Angelo Amante
ROME, Feb 6 (Reuters) - Mario Draghi's prospects of forminga government in Italy were boosted on Saturday when the twolargest parties in parliament, the anti-establishment 5-StarMovement and the rightist League, both gave him theirconditional backing.
However, Draghi's route to power is still not clear. Bothparties said his policy proposals would be the key to securingtheir support, and it may be some time before he is able to puttogether a coalition able to muster a parliamentary majority.
Having completed a first round of formal consultations withparties on Saturday, Draghi will hold more talks next week aimedat drawing up a cabinet, a broad policy agenda and establishingthe make-up of a ruling coalition.
The 5-Star Movement, the largest group in parliament,sounded more cautious than the League on Saturday. Its leaderVito Crimi set out a long list of green and left-leaning policypriorities it wanted to see from a future Draghi cabinet.
"We said we were open to considering whether the conditionsare right to join a government, we will decide above all on thebasis of the policies," Crimi told reporters after a 90-minutemeeting with the former European Central Bank chief.
Head of state Sergio Mattarella asked Draghi on Wednesday totry to form an administration after the previous one, led byGiuseppe Conte, was brought down due to the collapse of theruling coalition.
Matteo Salvini, the firebrand leader of the traditionallyeurosceptic League, sounded enthusiastic after his talks withDraghi, which lasted about half as long as 5-Star's.
The League was ready to join a government "that goes toBrussels keeping its head high in the name of the nationalinterest", Salvini said.
"Unlike others we don't think just saying no gets youanywhere," he said in reference to some parties' attempts toexclude the League. "The best interest of the country must comebefore any personal or party interest."
SHIFTING TOWARDS DRAGHI
The 5-Star Movement had initially ruled out backing Draghi,while Salvini has repeatedly shifted his position, first callingfor snap elections, then saying the League would not govern with5-Star, before his latest "no vetoes" stance.
Italian financial markets have rallied on the expectationDraghi will succeed. Last week Italy's 10-year bond yield postedits biggest weekly drop since July, while the gap over theGerman Bund yield narrowed to its lowest in five years.
Investors hope the man widely credited with saving the euroduring the 2012 sovereign debt crisis can spearhead reforms toboost growth in a country that has long underperformed itsEuropean peers, weighing down the whole euro zone.
While almost all the parties in parliament have now saidthey are potentially willing to back Draghi, it remains to beseen whether they are willing to do so together, creating abroad, cross-party coalition.
The centre-left Democratic Party has said it does not wantto govern with the League, while Crimi also signaled he wanted anew coalition to be based around the left-leaning and centristforces that formed the last one.
Silvio Berlusconi's centre-right Forza Italia party, thefourth largest in parliament, gave its unconditional backing toDraghi after meeting him on Friday, but it is not clear if5-Star would govern with Forza Italia, a sworn political enemy.
5-Star, born as an anti-system, anti-euro protest party, isnow internally divided, with many of its members uneasy aboutthe prospect of backing a former ECB president.(Additional reporting by Valentina Consiglio; Writing by GavinJones; Editing by Valentina Za and Christina Fincher)