If the Freedom Party (FPOe) and Norbert Hofer "are going to fantasise about an EU exit, they are playing with fire," Alexander Van der Bellen, 72, told the Oesterreich daily.
The far-right "has been flirting for years with leaving the EU and the eurozone... I am going to make it an issue (in the campaign), of course, whether Hofer and the FPOe like it or not".
Hofer, 45, and the anti-immigration FPOe have toughened their stance on Austria's membership of the European Union in the wake of Britain's June 23 vote to leave the bloc.
"If the EU develops in the wrong way, instead of returning to its actual basic values, if it becomes more centralised, and if Turkey joins, then for me it would be time to say that Austrians must also be asked (about membership)," Hofer said after the "Brexit" vote.
A poll published by Oesterreich on Friday, albeit of only 600 people, found 52 percent of those surveyed were against Austria leaving the EU, 30 percent in favour and 18 percent undecided. Sixty percent opposed a referendum.
Van der Bellen beat Hofer in a run-off on May 22 but by only 30,000 votes, and a far-right legal challenge succeeded in getting a court to annul the result because of procedural errors. A new vote is on October 2.
Traditionally the Austrian head of state's job has been largely ceremonial but Hofer has indicated that he would make use of hitherto untapped powers afforded under Austria's constitution.
Hofer becoming the EU's first far-right president would also be of enormous symbolic importance for the FPOe two years before the next scheduled general election, and be a fillip to other populist parties in Europe.
Van der Bellen's comments came on the day he was meant to be sworn in if his May victory had not been declared null and void, with incumbent Heinz Fischer formally stepping down in a ceremony on Friday.
Fischer has been replaced on an interim basis by the speaker of parliament Doris Bures and her two deputies, one of whom is Hofer. He has rejected calls to step down from this post during the campaign.