* Centrist cabinet resigns, to stay on in caretaker role
* Social Democrats woo conservatives, who keep distance
* Disarray could last months in affluent EU state
VIENNA, Oct 1 (Reuters) - Austria's government formally resigned on Tuesday but will stay on in a caretaker role as wary conservatives consider whether to renew a coalition with the centre-left after they suffered big losses to the far right at weekend elections.
Chancellor Werner Faymann's Social Democrats (SPO) are putting all their efforts into forming another coalition with their People's Party (OVP) junior partners to keep power with the mainstream parties that have dominated post-war politics.
But the OVP was keeping a frosty distance from Social Democrat suitors, mulling alternatives after the two big pro-Europe parties were reduced to a flimsy majority in a parliamentary election that buoyed the eurosceptic far right.
Stung by the partners' worst showing since 1945 and facing some internal resistance to another "grand coalition", OVP leader Michael Spindelegger was looking at options including leading a bloc with the rightist Freedom Party (FPO), which got over a fifth of Sunday's vote - and another smaller party.
The outgoing cabinet was asked by President Heinz Fischer to stay in a caretaker capacity until a new government is formed. Faymann was to return to the Hofburg presidential palace later on Tuesday for talks with Fischer, who has made clear he wants to see a two-party coalition emerge.
But the political uncertainty could run for months, delaying tax, pension and education reforms that analysts say are needed to preserve the Alpine republic's prosperity.
A long standoff could also boost the fortunes of the anti-foreigner and anti-Islam FPO led by Heinz-Christian Strache, who rails against bailouts of euro zone laggards and plays to fears that asylum-seekers will leech off hard-working Austrians.
Faymann has ruled out including the FPO in a coalition, so would have to get the environmentalist Greens, car parts magnate Frank Stronach's eurosceptic party and the new Neos liberal bloc all on board should the OVP ditch the SPO.
Spindelegger could ask either Stronach or Neos to join an OVP-FPO government. One senior OVP aide said he was betting on continuing the centrist coalition that has governed since 2006, but added: "Politics is full of surprises."
Spindelegger was to have his own meeting with Fischer on Wednesday. The president traditionally asks the biggest party in parliament to form a government, a step expected for next week.
OVP power broker Erwin Proell, governor of Lower Austria province, told ORF radio he still thought a fresh coalition with the SPO made sense if the squabbling allies - badly split over tax and education policy - could find a way to cooperate.
A two-party government was surely better than one with three or four partners, he said, heaping scorn on Stronach, whose party got nearly 6 percent of the vote.
"Why would you want to form a government with someone who fears the Chinese could attack us? This is ludicrous," Proell said, citing Stronach's comment during a debate that Austrian neutrality meant little if the country was invaded by Chinese.