Like Trump as well as other populist groups in Europe, the FPOe has boosted support by stoking concerns about immigration.
The two candidates in Austria's longest ever presidential race clashed Sunday over the European Union, Donald Trump, and migrants as they faced off in a TV duel a week before the runoff.
Greens-backed contender Alexander Van der Bellen accused his far-right rival Norbert Hofer of stirring insecurity by threatening to pull Austria out of the EU.
Hofer of the anti-immigration Freedom Party (FPOe) has said he would call a referendum on EU membership if Turkey joined the 28-member club or if Brussels tried to centralise power further.
"The FPOe has been toying with Austria's exit for 20 years. Many politicians in Europe are worried that the mere speculation could trigger... an avalanche of right-wing populism," said 72-year-old Van der Bellen during the live debate broadcast on private channel ATV.
"The most important thing is the solidarity between member states, otherwise we won't be able to assert ourselves in the face of Russia or the United States."
But Hofer, 45, dismissed the allegations as media-led "scare-mongering".
"There won't be an 'Oexit'. I've repeatedly said that I want a positive development of the EU," he said.
While Van der Bellen stressed Austria's important relationship with its largest trade partner Germany, Hofer vowed to seek closer ties with eastern and central European neighbours and, primarily, Russia.
He denounced German Chancellor Angela Merkel for "causing serious damage to Europe" with her open-door policy, which he said has allowed hundreds of thousands of migrants "including terrorists to trek through Austria" since last year.
Hofer also attacked Van der Bellen for criticising the US election win of Donald Trump.
"It is not clever to describe a president as a rabble rouser," he said.
Van der Bellen hit back saying politicians across Europe felt "anxious" about the arrival of a US president-elect who has been accused of sexist attacks on women and threatening the rights of minorities.
Like Trump as well as other populist groups in Europe, the FPOe has boosted support by stoking concerns about immigration and what it portrays as an out-of-touch elite.
Hofer hopes to become the EU's first far-right head of state on December 4, after nearly 350 days of campaigning.
In May, he lost by a paper-thin margin to Van der Bellen, but the FPOe got the result overturned due to procedural errors. A re-run set for October was again postponed because of faulty glue on postal vote envelopes.
Opinion polls suggest next Sunday's race is too close to call.
Hofer said he would not contest the outcome this time.
"It won't happen again, I can guarantee it. The whole world will be watching us," said Hofer.
The largely ceremonial role of president still carries considerable cachet, and Hofer's win would likely be a major boost to the far-right both in Austria and further afield.