The election pits Norbert Hofer, seeking to become Europe's first far-right president since 1945, against independent ecologist Alexander Van der Bellen.
The post of Austrian president is largely ceremonial but a win for Hofer and his Freedom Party (FPÖ) would be a major symbolic victory for populists across Europe ahead of several elections in 2017.
Hofer, 45, appeared to accuse Van der Bellen, 72, of being a spy for the Soviet Union during the Cold War, citing claims made in a book written by a former Austrian security official.
"That is the most appalling thing I have heard in a long time," Van der Bellen said. "If I had known about these claims in the book we would have sued... It's ridiculous."
Van der Bellen meanwhile said that Hofer and the FPÖ wanted to pull Austria out of the European Union, prompting Hofer to call him a "liar".
Hofer has said that he will press for a referendum on Austria's EU membership if Turkey joins the bloc or if the 28-nation group becomes too centralised.
Hofer said that Van der Bellen had insulted US president-elect Donald Trump. Van der Bellen said that he had been appalled by the "sexist comments" made during Trump's campaign for the White House.
Hofer and Van der Bellen are due to hold their final campaign events on Friday, with opinion polls suggesting the race is too close to call.
The election is a re-run of the presidential poll held in May, when Van der Bellen beat Hofer by just 31,000 votes. The FPÖ managed to get the result of that vote overturned due to procedural irregularities.