As the European music competition got underway on Tuesday night the internet broadcast was interrupted by footage showing missiles pounding the streets and menacing music played in the background.
Kan said hacking of the website did not affect the standard television relay of the show in Israel or abroad.
Israel's hosting of the 2019 version of the European music competition comes as fierce fighting raged in the Gaza strip earlier this month with Hamas.
Kan played down the hack, noting that the evening ended without further incident as Greece, Belarus, Serbia, Cyprus, Estonia, Czech Republic, Australia, Iceland, San Marino and Slovenia made it through to Saturday's finals.
'We know that at a certain stage there was an attempt, apparently by Hamas, to commandeer our digital broadcast,' Kan CEO, Eldad Koblenz, told Israel's Army Radio.
'But I am happy to say that within a few minutes we managed to assume control over this phenomenon.'
Hamas, a Palestinian Islamist group that controls the Gaza Strip, had no immediate comment.
Earlier this month it engaged in three days of fighting with Israel that included hundreds of rocket attacks from Gaza and Israeli air strikes in the enclave.
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