Herbert Kickl told a news conference he wants "basic services centres, suitable infrastructure that enables us to concentrate people in the asylum process in one place".
The comments quickly provoked outrage, with Alexander Pollak, head of migrants charity SOS Mitmensch, calling it a "deliberate provocation" and left-wing essayist Robert Misik saying "a Rubicon has been crossed".
The opposition Green Party warned against the "language of National Socialism creeping into our way of thinking and feeling", while the NEOS party said Kickl must apologise for his "deliberate provocation".
Kickl, who became interior minister last month when his Freedom Party (FPÖ) formed a coalition with the centre-right following elections in October, back-peddled, saying he did not "intend to provoke anyone".
He said the government would implement a "very, very strict asylum policy" in response to what he said was a rise in crimes committed by foreigners last year.
The head of the FPÖ, Vice-Chancellor Heinz-Christian Strache, also caused unease this month by appearing to suggest that asylum-seekers should be kept in empty military barracks and subject to an evening curfew.
The party was formed by former Nazis in the 1950s. In the 1990s it was headed by Jörg Haider, whose many controversial comments included calling Hitler's employment methods "orderly".
On Wednesday, Austria's main Jewish Religious Community (IKG) organisation said that it would continue to shun any contact with the FPÖ, including with government ministers from the party.