In an interview on ORF radio's Morning Journal on Thursday, Kurz (ÖVP) outlined a five-point plan to address the situation.
Key to the minister's proposal is creating awareness among Austria's Muslim youth.
This must happen urgently "in Islamic groups, prayer houses and mosques," said Kurz, "because young people need to know that jihad is not a game but deadly serious and that the main victims of the IS-terrorists in Iraq and Syria are Muslims."
The non-Muslim majority of the Austrian population also need to be educated, Kurz said, noting the current general suspicion against Austria's 500,000 Muslims, despite the best part of this group being well integrated.
The Integration Minister reiterated his call to Islamic religious teachers, describing them as the "antennas to young people".
They should take preventive action, Kurz said, by explaining to young people that faithful Muslims should not do such things.
Religious teachers should also report problems.
Kurz also demanded the City of Vienna take more control in purely Islamic kindergartens, ensuring German language is also taught.
The Foreign Minister also reiterated his plan to raise awareness of how internet platforms such as Facebook and Youtube are used to discuss the topic of jihad and plans to forge an alliance with other countries to put pressure on the two companies.
Germany and other European countries are already on board with this proposal, he said.