Austrians voted Sunday in a key presidential runoff which could usher in the European Union's first extreme right-wing leader amid the continent's worst post-war migrant crisis.

A huge influx of asylum-seekers, growing unemployment and frozen reforms have left Austria deeply polarised and driven angry voters away from the centrist ruling coalition toward fringe groups.

For the first time since 1945, the president will not come from one of two main parties, prompting national media to warn of a political "tsunami".

Instead, the showdown pits 45-year-old Norbert Hofer of the anti-immigration Freedom Party (FPOe) against the Green-backed economics professor Alexander van der Bellen, 72.

Polling stations opened at 0500 GMT and the first results are expected at 1500 GMT. Final results will be announced on Monday after postal votes have been counted.

They could prove to be a tie-breaker in the race, with close to 900,000 people -- or a record 14 percent of Austria's 6.4 million eligible voters -- casting their ballot by mail this year.

Last month, Hofer -- a gun enthusiast left partially disabled after a paragliding accident -- comfortably beat his rival by 35 percent to 21 percent.

- 'Pest and cholera'

Leaning on his trademark cane, the far-right hopeful was confident of victory in his final public address on Friday.

"I will be your new president," he told a jubilant crowd at the Viktor-Adler square in Vienna's Favoriten district, an FPOe stronghold.

Hofer's win would also pave the way for the FPOe to head the next government after parliamentary elections, scheduled for 2018.

Although no official surveys were released ahead of the vote, Austrian betting agencies indicated Saturday that Hofer maintained a slight lead over his opponent.

Former Green Party leader Van der Bellen has proven as divisive a figure as Hofer, with conservative Austrians accusing him of pandering to the left.

"It's a choice between pest and cholera. Whoever wins, I will wake up on Monday to somebody whom I don't want to represent Austria," said a mother-of-two in her thirties, refusing to give her name, after casting her ballot in Vienna.

"I've chosen the lesser the lesser evil, but it's a frustrating election," another voter, Astrid Meister, told AFP.

- 'I don't like them' -

Described as the FPOe's "friendly face", Hofer has pushed populist themes with a winning smile instead of the inflammatory rhetoric used by his close ally, party leader Heinz-Christian Strache.

He has focused on Austrians' social-economic wellbeing and insisted he would not push to leave the EU unless Turkey joined the bloc.

The more moderate approach paid off, earning the FPOe its best result at federal level last month.

But observers warn that beneath Hofer's smooth image lurks a "wolf in sheep's clothing", who has already threatened to seize upon never-before-used presidential powers and fire the government if it fails to get tougher on migrants or boost the faltering economy.

European leaders including European Commission chief Jean-Claude Juncker have also voiced concern at the turn of events in Austria.

"The prospect of seeing the far-right win forces me to say that I don't like them," Juncker told French newspaper Le Monde on Friday.

"The Austrians don't like to hear this but I don't care: there is no debate or dialogue with the far-right."

- Lacklustre protests -

For now, the criticism echoes through Vienna, where anti-Hofer protest calls have failed to draw large crowds.

Back in 2000, more than 150,000 people marched in the Austrian capital against the FPOe -- then led by the late, SS-admiring Joerg Haider -- after it entered a much-maligned coalition with the OeVP.

The far-right power grab also prompted international sanctions and turned Austria into an EU pariah.

But times have changed, with support for populist parties surging across the continent.

Marine le Pen of France's Front National saluted Hofer's performance, saying it "was in line with history".

Van der Bellen, a distinguished economist with backing from many public figures including new Chancellor Christian Kern, warned Hofer's presidency would pose a threat to democracy and vowed to not swear in Strache as chancellor.

"I've experienced how Austria rose from the ruins of World War II, caused by the madness of nationalism," he said.

"This election is a pathbreaking decision between a cooperative and an authoritative style".