MADRID (Reuters) - Acting Prime Minister Mariano Rajoy moved a step closer to breaking Spain's 10-month political deadlock on Monday as a regional powerhouse of the main opposition party backed allowing him to form a new government by abstaining in a confidence vote.

The Socialists' federation in the southern region of Andalusia said it supported abstention to head off a third parliamentary election in a year.

Its head, Susana Diaz, is favorite to replace Pedro Sanchez as national party leader, suggesting Socialist federations in other regions could follow her lead.

"There is unanimity (within the federation) to avoid a third election and abstention is the only way," said the party's deputy leader in Andalusia, Juan Cornejo, after a meeting on Monday.

Rajoy's conservative People Party (PP) finished first in Spain's two most recent elections, in December and in June, but failed each time to win an absolute majority.

The Socialists, who came second both times, have so far refused to vote in favor of a Rajoy-led administration or abstain to allow him to run a minority government, prolonging the political limbo.

Sanchez stepped down as Socialist leader this month amid rising criticism within the party over his response to the impasse.

Its senior members will meet on Oct 23 to decide whether to back Rajoy or abstain in a parliamentary confidence vote that must take place by the end of the month to avert another national election in late December.

If the Socialists continued to oppose Rajoy, they would slip to third place in that election behind the anti-austerity alliance Unidos Podemos, and Rajoy's support would rise enough for him to form a coalition government, a poll showed on Sunday.

Diaz's bid to succeed Sanchez is backed by the heads of the Valencia, Extremadura and Castilla-La Mancha regions. Extremadura's federation also said on Monday it supported abstaining to allow Rajoy to serve a second term.

(Reporting by Carlos Ruano; Writing by Angus Berwick; Editing by John Stonestreet)