Kurz has repeatedly harked back to Austria's past as the 80th anniversary approaches of the country's annexation by Nazi Germany, urging citizens not to forget "the sad and shameful days of March 1938," when Nazi troops marched in to a rapturous welcome.
On Saturday he posted a hard-hitting tweet that read: "Austrians were also actors and were associated with atrocious crimes of the Holocaust.
"We bear a clear historic responsibility that the new government clearly recognises," he said.
Six million Jews were killed in the Holocaust during World War II, many of them in gas chambers in Nazi death camps.
Kurz's comments come against the backdrop of an rise in anti-Semitic acts and speech in Austria.
This week, prosecutors charged four members of a student fraternity behind a songbook containing lyrics celebrating the Holocaust and other Nazi atrocities.
The lyrics of one song ran: "'Step on the gas, old Germanics, we can make it to seven million'."
The fraternity's members include a candidate from the far-right Freedom Party (FPÖ) who is contesting in a state election on Sunday in Lower Austria.
The revelations sparked a wave of indignation across the country.
The United Nations in 2007 designated January 27th as International Holocaust Remembrance Day to mark the 1945 liberation of Auschwitz-Birkenau, the largest of the Nazi death camps.