"It is clear to me that Austria must play an important role within the European Union and when we are pro-European, we should not only stand for Europe but be an especially active participant in Europe," the 31-year-old conservative "whizz-kid" said.
"This is clearly what I will do in the coming years," he added.
Kurz's People's Party (OeVP) won 31.5 percent of the vote on Sunday, near-complete results show, and his most likely coalition partner is seen as the populist Freedom Party (FPOe), which came in third on 26.0 percent.
It wants EU sanctions on Russia lifted and for Austria to potentially join the Visegrad group of eastern and central European countries that has become a thorn in Brussels' side.
Kurz said he would visit Brussels on Thursday, saying he "deliberately" chose the EU capital for his first foreign trip after the election. He is due to meet Jean-Claude Juncker and Donald Tusk, the respective presidents of the European Commission and the European Council.
Kurz could be given the go-ahead to form a new government as early as Friday.
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