The result of Sunday's presidential election is still too close to call and around 850,000 postal votes are still being counted. The final result will be known later on Monday.
Green candidate Alexander Van der Bellen needs to win roughly 62 per cent of them to catch the far-right politician Norbert Hofer.
The Austrian public broadcaster ORF predicts Van der Bellen will win by just 3000 votes, whereas ATV predicts Hofer, of Austria's far-right Freedom Party, by 20,000.
For the first time since World War II, both the main centrist parties were knocked out in the first round.
The migrant crisis was the key issue in the campaign although Hofer has also taken a strong line against the EU, stating, "We will not take orders from Brussels or Berlin."
Austrian Socialist MEP Karoline Graswander-Hainz is among those who have expressed fears of a Hofer victory, saying, "A victory for Hofer could not only be dangerous for Austria, but also for Europe."
Graswander-Hainz, an MEP for Austria's ruling Social Democratic Party, said, "During interviews or discussions he tries to keep the image of a nice, smart, likeable, young and fresh candidate who understands the citizens and their fears, but if you see him talking in front of his own party and their members Norbert Hofer shows his real face: anti-European, against refugees, against foreigners."
Hofer is a 45 year-old aeronautical engineer turned politician for Austria's far-right Freedom Party who has said in the past that carrying guns is a "natural consequence" of immigration. He has also posted pictures of him and his four children on gun ranges.
He recently said that he understood the rising gun ownership in Austria, "given current uncertainties."
He has also been reportedly spotted wearing the blue cornflower, which is an old clandestine Nazi symbol that harks back to ideas of pan-Germanism.
Some 90,000 people claimed asylum in Austria last year, equivalent to
about one per cent of the Austrian population, and the Freedom Party has run a campaign against immigration.
The presidency is a largely ceremonial post but a Hofer victory could be the springboard for Freedom Party success in the next parliamentary elections, scheduled for 2018. If elected he could, in theory, dismiss the current government, a Social Democrat and Christian Democrat coalition.
The prospect of Hofer's election raised concerns in Austria and in the EU as it would mark the first one of a far-right head of state by universal suffrage in Europe.
Such concerns could explain why turnout in the second round (71.9 per cent) was higher than in the first round (68.5 per cent) .
Graswander-Hainz, a member of the committee on international trade, says the election shows that mainstream parties have to do more to combat the growing appeal of right-wing populism.
"It is of utmost importance now to listen carefully to our citizens' concerns, their sorrows and their fears to regain trust towards politics and deliver practical solutions to combat the current problems," she says.
Graswander-Hainz thinks the stakes could not be higher, adding, "We need to protect our democracy, the rule of law and our European values. If we do not succeed, these movements will destroy our European democracy."