Prime Minister Giorgia Meloni told her Brothers of Italy party on Tuesday that it should expunge from its ranks anyone who idolises Italy's fascist past.
Her call came after an undercover media investigation last week released a video of members of her party's youth wing making fascist salutes and chanting "Sieg Heil".
In a letter to party leaders, Meloni said she was "angry and saddened" that their actions damaged the group's reputation.
"There is no room in Brothers of Italy for racism or antisemitism, nor is there space for those who are nostalgic for the totalitarian regimes of the 20th century or for any manifestation of foolish folklore," she wrote.
"Our task is too great for those who have not understood its scope to be allowed to ruin it."
Brothers of Italy traces its roots to a neo-fascist group set up after World War Two, but Meloni herself has looked to distance herself from the far right in recent years and says her party is mainstream conservative.
Opposition parties leapt on the investigation by the online newspaper Fanpage. They said it showed Brothers of Italy was a refuge for extreme right-wingers, belying Meloni's efforts to present a moderate image both at home and abroad.
Meloni, who last week denounced the newspaper's undercover methods, said on Tuesday that Brothers of Italy had to be transparent and consistent.
"Anyone who believes there can be a public image of Brothers of Italy that does not correspond to their private behaviour simply does not understand what we are, and thus is not welcome among us," she said.
Fanpage published clips of youth members chanting "Duce", a reference to Italy's fascist leader Benito Mussolini. It also showed a group chat where someone had posted the message: "Jewish people are a race and I despise them."
Two youth members resigned last week after the second instalment of the expose was released.
