Sanctions for debt-laden EU members "will prevent Italy, for example, ending up a second Greece thanks to irresponsible debt policies", the centre-right leader told Italy's La Stampa newspaper.
This is the only way "we can avoid Italy putting the entire eurozone at risk", Kurz said, targeting Italy's big-spending populist coalition government.
Italy's public debt is currently around 2.3 trillion euros ($2.6 trillion), or 132 percent of Italy's GDP – way above the 60 percent EU ceiling.
The ruling coalition of the anti-establishment Five Star Movement (M5S) and anti-immigrant League party has also increased the budget deficit since coming to power last June as it implements big-spending election promises, including tax cuts and generous income support.
League leader Matteo Salvini has expressed interest in joining the conservative European People's Party (EPP) bloc in the European parliament, of which Kurz's centre-right People's Party (ÖVP) is also a member.
Kurz on Friday expressed scepticism over any cooperation between the EPP and parties further to the right in the European Parliament, including the League.
"We don't want to hand over the EU to the extreme fringes on the left or right, we need instead a strong politics of the centre," he told Austrian newspapers.
The League is hoping to make significant gains in the European parliament elections on May 26th.
Kurz has previously called for the renegotiation of the European Union's Lisbon Treaty and tough action against countries with high debt and those letting illegal migrants transit ahead of the EU elections.
At home the ÖVP has been in coalition with the far-right Freedom Party (FPÖ) since elections in late 2017, but in recent weeks Kurz has come under increasing pressure to condemn the actions of some FPÖ members.
The "spread" – the different between yields on 10-year Italian government debt compared with those in Germany – was up from 253 on Friday to 260 points on Monday, which analysts said was partly because of the Kurz interview.