Half of the deportees died beaten, gassed, shot or worked to death in granite quarries and armaments factories.
Founded by former Nazis in the 1950s, the Freedom Party (FPOe) is currently in third place with 24 percent in surveys of voter intentions, behind the Social Democrats (SPOe) with 27 percent and the centrist People's Party (OeVP) with 32 percent.
Neither of the two leading parties has ruled out forming a coalition with the FPOe, which has spent the last few years polishing its extremist image under leader Heinz-Christian Strache.
But for the Mauthausen Committee, the far right still shares a "distinct closeness to Nazi ideology".
"If someone wants to share power with the FPOe, they can't pretend afterwards that they didn't know about their diehard attitude," committee chairman Willi Mernyi said in a statement Wednesday.
His organisation was created in memory of the 200,000 prisoners who passed through the Mauthausen concentration camp in northern Austria during World War II.
Half of the deportees died -- beaten, gassed, shot or worked to death in granite quarries and armaments factories.
The committee said the FPOe continued to stoke scandals "with a Nazi whiff", citing at least 60 anti-Semitic and racist incidents involving FPOe politicians since 2013.
"They may be isolated cases but they aren't rare or atypical," it said in the statement.
The FPOe hit back, accusing the committee of "dirty campaigning".
"Those seriously concerned about anti-Semitism in Austria should long have focused on the consequences of the new mass migration... of people flooding into Austria from cultures for which anti-Semitism is virtually part of the daily agenda," the party's general secretary Herbert Kickl said.
The FPOe, like other populist parties in Europe, has seen its support rise on the back of concerns about immigration and terrorism.
Last December, the party's smooth-tongued candidate Norbert Hofer narrowly missed becoming the EU's first far-right head of state after losing a run-off election.
But the party has faced pressure with the advent of the OeVP's hugely popular new chief Sebastian Kurz.
Kurz, a 30-year-old conservative who was a key force behind the closure of the western Balkan migrant route last year, has bolstered support for his party since taking over the reins in May.
Analysts say it is not unlikely that the OeVP, in case of a victory in the October 15 ballot, could opt for a coalition with the far right.
Both parties had previously shared power between 2000 and 2005, sparking international protests.