Founded by ex-Nazis in the 1950s, the Freedom Party (FPÖ) is fighting for second place with the Social Democrats in surveys of voter intentions, behind the conservative People's Party (ÖVP).
Neither of the two leading centrist parties has ruled out forming a coalition with the FPÖ, which has sought to polish its extremist image under leader Heinz-Christian Strache in recent years.
Van der Bellen -- who beat a far-right opponent to the presidency last year -- has previously vowed he would not appoint Strache as chancellor if the FPÖ wins on October 15th.
Although the head of state holds a largely ceremonial role, he nonetheless has the power to fire the government or refuse to swear in a leader.
"I will make sure after the election that the new government, whatever it looks like, does not lose sight of one thing: Austria should also in the future be a country at the heart of Europe, at the heart of the European Union," Van der Bellen said in a rare address to the nation on Tuesday.
"(It should be) a country, in which cooperation, mutual respect and the core values anchored in the constitution remain the compass of our actions," the 73-year-old added.
Van der Bellen also insisted that immigration was one of the bloc's "most pressing problems" that could only be solved on "a European level".
The eurosceptic FPÖ, like other populist parties in the EU, has seen its support rise on the back of concerns about immigration and terrorism, fuelled by the continent's worst migration crisis since 1945.
While the far-right has toned down its anti-EU rhetoric for next month's vote, it openly targets refugees and warns of Austria's "Islamisation".
However, the FPÖ has faced pressure with the recent arrival of the ÖVP's popular new chief Sebastian Kurz.
The 31-year-old was a key force behind the closure of the western Balkan migrant route last year and has bolstered support for his party since taking over the reins in May.
Analysts say it is not unlikely that the conservative ÖVP, in case of a ballot victory, could opt for a coalition with the far-right.
Both parties had previously shared power between 2000 and 2005, sparking international protests.