By Shadia Nasralla and Kirsti Knolle
VIENNA (Reuters) - Austria will re-run a presidential election run-off on Oct. 2, giving far-right eurosceptic candidate Norbert Hofer the chance to reverse a wafer-thin defeat, this time in the shadow of Britain's vote to leave the European Union.
Hofer and his FPO (Freedom Party) have already raised the prospect of Austria holding a similar referendum, yet political analysts say the tactic risks foundering on a deep bedrock of support for European integration.
Hofer, 45, lost out in May by just 31,000 votes to pro-European former Green Party leader Alexander Van der Bellen, 72, narrowly failing to become the EU's first far-right head of state.
But Austria's highest court annulled the vote, finding that sloppiness in the count, while not intended to manipulate any votes, had potentially been serious enough to change the outcome, and required a re-run.
Social-Democrat Chancellor Christian Kern said the vote would be re-run on Oct.2.
"The EU will be a central topic. Both candidates are clearly positioned and Brexit made this issue even more timely," said political science professor Anton Pelinka.
"Who will benefit from this? Probably Van der Bellen, because a majority of Austrians are for Austria staying within the EU, despite all the euroscepticism."
Britain's vote has been welcomed by eurosceptic far-right parties including the FPO's ally, France's National Front.
But Hofer has set specific conditions for calling an EU referendum in Austria that seem unlikely to be met in the short term: Turkey joining the EU, or the bloc turning into "a centralized government that deprives its member states of their power and drops the principle of unanimity on major issues".
Political analyst Peter Filzmaier saw the FPO's failed campaign against joining the EU in 1994, when Austrians voted 2-to-1 for membership, as a deterrent to a full-blown exit campaign.
"Hofer will try to play tactically with this, he will repeatedly criticize the EU sharply, but stop short of demanding an immediate exit," Filzmaier said.
FPO head Heinz-Christian Strache said an Austrian exit - or "Oexit" - could be an option "if the EU continues to run itself into the ground and is not capable of learning that people want an economic union that involves its citizens".
But the pro-EU Van der Bellen said he expected to benefit from Britain's vote, which the International Monetary Fund has said could shrink the British economy by up to 4.5 percent by 2019:
"The (British) economy will slump enormously, jobs will be lost ... I think a large majority of Austrians don't want Oexit or Brexit. Anyone who plays with this is playing with fire."
In a survey conducted by the EU last November, only 26 percent of Austrians said they trusted the EU, but 60 percent or more said they wanted more integration, not less - in the form of a European economic and currency union or joint European security, defense and foreign policies.
"If the FPO go with an 'Oexit' strategy inspired by Brexit, they might shoot themselves in the foot," said a Vienna-based diplomat. "The Austrians are not like the British, they are more European, they're not an island,"
Austria's president has only limited powers, which do not run to independently calling a referendum.
But Hofer's strong showing and the failure of the main coalition parties - the Social Democrats and the conservative People's Party - have already underlined how successfully the FPO is channeling fears about mass immigration and falling living standards.
Recent opinion polls put the FPO at over 30 percent, around 10 points ahead of both the ruling parties, although the next parliamentary election is not due until 2018.
(Editing by Kevin Liffey)