Turkey's long-stalled EU application is thought to still be some way off becoming a reality, however Kurz said he would reject the opening of further negotiating chapters that could potentially see Turkey move a step closer to joining the bloc.
"I have a say in the matter on the [European] Council of Foreign Ministers, where it will be decided if a new chapter will be opened with Turkey, and I am opposed to it," he told the Kurier daily newspaper.
8m-Austria`s FM Seb.Kurz has a vote in 500m-EU and oppose to 80m-Turkey EU membership.— erdeman (@scutarian) August 8, 2016
EU rules state that decisions taken by the council must be agreed upon unanimously.
Increase in Austrian Criticism
The latest development comes amid an increase in Austrian criticism towards Turkey over President Recep Tayyip Erdogan's reaction to last month's failed coup, which has seen thousands of army officials, academics and teachers arrested.
In particular, Erdogan's threat to re-introduce the death penalty has led to warnings from European leaders, who say such a move would jeopardize Turkey's EU accession.
"We have to face reality: the membership negotiations are currently no more than fiction," Austrian Chancellor Christian Kern told the Die Presse newspaper.
"We know that Turkey's democratic standards are far from sufficient to justify its accession," he added.
Reflecting the tensions between Vienna and Ankara, Austrian Defense Minister Hans-Peter Doskozil described Turkey as a "dictatorship," while Heinz-Christrian Strache, the leader of Austria's far-right Freedom Party, compared the current crackdown on the media and opposition in Turkey to the purges committed by the Nazi Party in Germany, following the Reichstag fire of 1933.
Concerns Over Migrant Deal
The tension between Turkey and some EU countries has led to concerns that the migration deal negotiated between the two parties could ultimately be scrapped.
Erdogan renewed threats to pull out of the deal, saying the migration agreement "will not be possible" if the EU does not grant visa-free travel to Turkish citizens.
"The European Union is not behaving in a sincere manner with Turkey," Erdogan told French newspaper Le Monde.
Erdogan accuses #EU of failure to keep migrant deal promises: 'When we say this out loud, the gentlemen (in the EU) get very uncomfortable.'— Fulya Özerkan (@FulyaOzerkan) August 2, 2016
"If our demands our not satisfied then the readmissions will no longer be possible," he added.
While EU officials had set July 1 as the timeline for Turkish visa liberalization, such a development was based on a series of conditions, with EU officials arguing that Turkey's anti-terror laws need to be adjusted before any visa changes can be made.