MADRID (Reuters) - The leadership of Spain's Socialists meet on Sunday to decide whether to enable their conservative rivals to form a minority government, thereby ending ten months of political deadlock.

With just under two weeks to go until a deadline to form a government, the Socialist gathering is widely seen as a make-or-break summit that will determine whether Spain will manage to avoid its third general election in a year.

The Socialists - who came second in two inconclusive elections last December and in June behind the conservative People's Party (PP) - have so far vetoed attempts by PP leader Mariano Rajoy to form a minority administration.

The rise of several newer forces such as anti-austerity Podemos ("We Can")in the wake of a long economic crisis splintered Spain's political landscape in the two ballots and left all parties well short of a parliamentary majority.

The prospect of a third election that could further drain support from the Socialists and alienate frustrated Spaniards has caused some senior members of the center-left force to change tack, however, causing a deep rift in the party.

Former Socialist leader Pedro Sanchez was ousted earlier this month over his handling of the impasse and his steadfast refusal to let the PP govern.

Since then, signs have mounted that the Socialists are now prepared to abstain in a confidence vote to allow Rajoy to form a new government, even if they still refuse to enter a coalition with his party and may block his policies in future.

The Socialists' federation in the southern regional bastion of Andalusia said on Monday it supported such an abstention, suggesting the rest of the party could be ready to shift its stance.

"We have to find the least bad solution," Javier Fernandez, the interim Socialist party head, told a parliamentary meeting on Tuesday, adding that another national election would likely benefit the PP.

Spanish politicians have until Oct. 31 to form a government. If they fail to reach an agreement by then, a fresh election will automatically be triggered.

Even if Rajoy does manage to form an administration with an abstention from the Socialists, focus will immediately turn to how stable his minority government is likely to be when budget cuts are on the cards for next year as Spain strains to reach its deficit targets.

(Reporting by Inmaculada Sanz and Sarah White; Editing by Angus Berwick and Ralph Boulton)