Hajduk Split, who won the game 2-1, in a statement apologised to UEFA and Ajax who "witnessed scenes which we do not want Europe to remember", while the Croatian football federation also condemned the incident.
Croatian leaders have slammed pro-Nazi and anti-Semitic chants by Hajduk Split football fans ahead of their UEFA Conference League match against Ajax, while Israel's embassy voiced shock.
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Groups of Hajduk Split fans, known as the Torcida, marched through the coastal town ahead of Thursday's match chanting: "Crush the Jews", "Rise up Adolf (Hitler)" and "Let's go Ustasha", referring to the country's World War II pro-Nazi regime, local media reported.
Dozens of fans were detained ahead of Thursday's match for violence. During the match Torcida fans set off flares and other pyrotechnics in the stands, forcing more than a 10-minute stoppage.
An investigation was opened into the pro-Nazi chants and suspects are being detained, police said.
President Zoran Milanović condemned the incident as "unacceptable and shameful" in a statement on Friday.
He urged swift action against the perpetrators to "show that there is no place in Croatia for the glorification of Nazism and Ustasha ideology."
Israel's embassy in Zagreb, in a statement obtained by the AFP news agency, said it was "deeply shocked by the serious anti-Semitic incident that took place in Split".
Conservative Prime Minister Andrej Plenković also condemned "messages of anti-Semitism...completely at odds with the values we want to uphold in Croatian society".
Hajduk Split, who won the game 2-1, in a statement apologised to UEFA and Ajax who "witnessed scenes which we do not want Europe to remember", while the Croatian football federation also condemned the incident.
Croatia's ultra-nationalist hardcore supporters have tainted the country's image for years, notably by chanting pro-fascist slogans and displaying Ustasha symbols.
The regime killed and persecuted hundreds of thousands of ethnic Serbs, Jews, Roma and anti-fascist Croatians.
Croatia were docked a point by UEFA after their fans painted a swastika on the pitch in Split in 2015, ahead of a Euro 2016 qualifier with Italy.
The perpetrators were never found.
In recent years, the country has seen a growing tolerance for its pro-Nazi past and critics accuse authorities of failing to sanction the use of Ustasha emblems.