Kurz's comments came Tuesday as he spoke at a joint press conference after meeting Hashim Thaci, Kosovo's deputy prime minister and foreign minister.
He said: "We see radical tendencies everywhere in Europe, as well as the fight against it.
"In Austria, we have people who have gone to Iraq and Syria to support the terrorists there, and it is very important to be united in Europe in the fight against this kind of radicalism."
The Austrian minister said that he knew Kosovo had done much to fight extremism.
- 'Regional leader'
Thaci stressed that Kosovo had shown concrete steps to fight against extremism and radicalism in Kosovo.
He said: "Fortunately, there is a political and civil consensus on this regard.
"We had citizens, as well as all the countries of Europe, who went to war in Syria or Iraq, but I can say that Kosovo is a regional leader in the fight against extremism and radicalism."
The Austrian diplomat also met Prime Minister Isa Mustafa after holding talks with the President of Kosovo Atifete Jahjaga.
Jahjaga and Kurz attended the opening ceremony of an exhibition of the Austrian artist Leopold Forstner in the Mother Teresa Cathedral in Pristina during the visit.