Benjamin Netanyahu said in a statement that he spoke with Kurz by telephone on Monday and commended Austria for "preserving the memory of the Holocaust and its war against anti-Semitism" in recent years.
Kurz responded positively when Netanyahu invited him to Israel, according to the statement. Kurz claimed the win as final results announced by the Interior Ministry showed his People's Party had a comfortable lead with almost all the ballots counted.
Both Kurz's party and the right-wing Freedom Party — Kurz's most likely government coalition partner — campaigned on the need for tougher immigration controls, quickly deporting asylum-seekers whose requests are denied and cracking down on radical Islam.
German Chancellor Angela Merkel says she isn't "dramatically concerned" about differences on refugee policy after conservative leader Sebastian Kurz won neighboring Austria's election.
Merkel said she congratulated Kurz on Sunday. On Monday, she credited Kurz's "energetic" modernization of his Austrian People's Party for his success but said the strength of the right-wing Freedom Party is a "big challenge" for its Austrian rivals.
Merkel wouldn't say what governing coalition she would like to emerge.
Kurz has been outspoken on migrant issues and last year organized the shutdown of the Balkan refugee route. Merkel questioned whether there are significant differences, saying that to a large extent refugee policy is "not so contentious."
She added: "If he becomes Austrian chancellor, I will of course go into this more deeply, but I am not so dramatically concerned."
Hundreds of thousands of ballots must still be counted in Austria's general elections, but the tally is not likely to substantially change results that have put 31-year old Foreign Minister Sebastian Kurz on track to become Europe's youngest leader.
Near-final results of Sunday's elections that have already been announced do not include the absentee ballots and those cast by voters outside of their home districts. The Interior Ministry says it expects to have the more than 600,000 absentee votes counted by late Monday and the rest — between 50,000 and 100,000 — by Thursday.
The final tally could move Chancellor Christian Kern's Social Democratic Party to second place and relegate the right-wing Freedom Party to third. But the lead of Kurz's People's Party is not endangered.