Kurz's comments came as he and his ministers held a special joint session in the Austrian city of Linz with their Bavarian counterparts from the German CSU party, which is currently locked in a battle over migration policy within the government of Chancellor Angela Merkel in Berlin.
"We can't wait until we have a catastrophe like the one in 2015," Kurz said, referring to the migrant crisis of 2015-16, which saw more than 150,000 people seek asylum in Austria, a country of 8.7 million.
A row over migration policy in Germany between Merkel and her CSU interior minister Horst Seehofer has shaken the stability of the government in Berlin.
Kurz insisted he didn't want to take sides in an "internal German debate" but welcomed the fact that immigration was once again being discussed by EU leaders ahead of a summit later this month.
"If the discussion in Germany has an upside, it's that there's now a new dynamic on the European level, and that there's now a bigger chance that we finally see action in the EU," Kurz said.
Without naming Merkel he also aimed a shot across her bows by making clear what he thought were the results of her decision to welcome refugees to Germany in 2015.
Those who opened the borders in 2015 "are responsible for the fact that we have border controls between Austria and Bavaria, between Austria and Hungary, between Austria and Italy, and that the situation could get even worse", he said.
Kurz, who hails from the centre-right People's Party (ÖVP) went into coalition with the far-right Freedom Party (FPÖ) after an election last year in which both parties made a clampdown on immigration a central theme.
Kurz was foreign minister under the previous government and often boasts of his actions to close the "Balkan route" for migrants in 2016.
The head of Bavaria's state government, Markus Söder, emphasised that Munich and Vienna "have a common conviction and position" on the issue.
Kurz has said he intends to make migration a key theme when Austria takes up the EU's rotating presidency at the beginning of July and has been busy seeking allies for his stance.
Last week he announced that Seehofer, Austria's interior minister Herbert Kickl and Italy's new interior minister Matteo Salvini -- from the xenophobic Northern League -- had formed an "axis of the willing" to combat illegal immigration.
On Thursday Kurz will go to Budapest to attend a meeting of leaders from the four central European Visegrad states -- Hungary, Poland, Slovakia and the Czech Republic -- who have traditionally supported hardline policies on migration.