"The battle against anti-Semitism and our policy of zero tolerance against all anti-Semitic tendencies is very important to me," Kurz told the right-wing Israel Hayom newspaper.
"It is a clear pre-condition for the formation of any coalition under my leadership," the 31-year-old conservative told the paper, which is a firm backer of Israeli Prime Minister Benjamin Netanyahu.
Kurz's People's Party (ÖVP) 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 (FPÖ), third on 26.0 percent.
Austria's Jewish Community (IKG) organisation warned Kurz on Tuesday that a coalition with the FPÖ could see people with "anti-Semitic, racist and eurosceptic beliefs" influence the government.
"The FPÖ behaved itself during the election campaign. But what the FPÖ says and what the FPÖ does are two different things," IKG chief Oskar Deutsch said.
When the FPÖ last entered government, in 2000 under former head Jörg Haider, who praised Hitler's "orderly" employment policies and praised SS veterans, Israel suspended relations.
They were normalised in 2003 under prime minister Ariel Sharon and the FPÖ's party head since 2005, Heinz Christian Strache, has moved to soften its image and improve relations with the Jewish state.
Strache, 48, has visited Israel several times, the last time in April 2016 when he met members of Netanyahu's government and laid a wreath at the Holocaust memorial Yad Vashem.
Israel's foreign ministry stressed at the time that it was a "strictly private visit" that included no official meetings.
Before the election Strache wrote to Netanyahu that Israel "possesses the right to build wherever is required in the Land of Israel" and that Austria's embassy should be moved to Jerusalem.
Kurz said in the interview that "it is not the time to talk about such a sensitive question" as moving Austria's representation to the disputed city from Tel Aviv.
The FPÖ was created by ex-Nazis in the 1950s and campaigners say that incidents of anti-Semitism and racism by party officials continue.
Netanyahu congratulated Kurz in a telephone call on Monday night while calling for the fight against anti-Semitism to continue.
An Israeli official speaking on condition of anonymity said on Tuesday it was "premature to take any position while the Austrian coalition is not yet formed".
Kurz met Austrian President Alexander Van der Bellen on Tuesday afternoon. He is expected to give Kurz a mandate later in the week to form a government.