From 1942 to 1945 Ofner attended the Nazi-era National Political Institutes of Education in Traiskirchen near Vienna.
From 1983 to 1987, Ofner was Austrian Minister of Justice in the governments of Fred Sinowatz and Franz Vranitzky.
Despite efforts by Ofner, Rainer was extradited to Italy, shortly after his arrest in the Rudolfsheim-Fünfhaus district of Vienna.
During the Lucona affair, the then Minister of Justice Ofner actuated in a parliamentary debate the saying: "Die Suppe ist zu dünn.
"Meaning "The soup is too thin" in English, he meant that the evidence for an accusation was not sufficient.