"The federal government’s line is clear: no additional voluntary admission to Austria," Kurz told reporters at a press briefing.
He argued that Austria had one of the largest migrant populations in Europe per capita and first needed to integrate 30,000 jobless migrants who were likely to receive asylum status.
President Alexander Van der Bellen sided on Tuesday with Vice-Chancellor Werner Kogler who said Austria needed to accept a limited number of women and children from Greek island camps.
Debates over the need to share migrants among EU nations were pushed to the forefront last week after Turkey said it would no longer hold back Syrians trying to flee fighting to Europe. Thousands have since amassed on the border with Greece.