Though Ms Stenzel is Catholic, she also has Jewish roots via her mother. Her great-grandfather was a rabbi and grandfather a cantor. In a 2006 interview, she said she took with her “the best from both sides” of her Catholic-Jewish upbringing.
Previously a journalist, she became an eccentric figure in the centre-right People’s Party before crossing over to the FPÖ in 2015.
In April, she compared leading TV journalist Armin Wolf to a Nazi-era judge.
In a statement, Ms Stenzel claimed she would not have attended if she had known beforehand that members of the Identitarian Movement would also be at Saturday night’s rally.
But Jewish community president Oskar Deutsch said her attendance showed “what kind of person she is.”
Politicians from the Social Democrats as well as the People’s Party also called for her resignation.
Ms Stenzel’s speech brought the FPÖ’s political extremism back into focus, three weeks before Austria’s next general election takes place.
It was the twelfth case of extreme-right activity inside the party since the coalition government it partnered was dissolved in May.