Sydney United 58 are pledging to track down fascist fans as the club is hit by a catch-all notice from soccer's hierarchy.
Football Australia (FA) has a broad brush of sanctions available under a show-cause notice issued in the aftermath of Saturday night's Australia Cup final.
NSW Premier Dominic Perrottet says the offensive fans must be banned for life.
"It was absolutely horrendous," he told reporters on Monday.
"It has no place, not just at sporting games, but anywhere in our state, and I know the police are looking at it.
"Those people who have done that through those salutes should be banned for life."
Sydney United condemned the behaviour of some spectators, saying they did not reflect the "wider views of the club" and its fans.
"Sydney United 58 FC has zero tolerance towards any form of disrespect, racism or discrimination and is working closely with authorities to conduct a full investigation," a club statement said.
"The club strongly condemns any behaviour that does not reflect the wider views of the club and its loyal supporters."
United are co-operating with the FA, who have issued the club with a show cause notice detailing "a number of alleged infringements".
"The club has separately been also asked to help identify individuals who displayed anti-social and harmful behaviour," FA said in a statement.
NPL NSW side United were the first non A-League Men's team to reach the cup final but that achievement - which culminated in a 2-0 loss to Macarthur FC - was tarnished by a section of spectators.
Some followers of United, formerly known as Sydney Croatia, sang Za Dom Spremni (For Homeland - Ready) - a chant used by the far-right Ustase movement in Croatia in the 1930s and 1940s.
United said such spectators had no place at their games.
"The club is deeply committed to creating an environment that is respectful and inclusive which also allows our community members to celebrate their heritage in a meaningful and responsible way," a statement said.
"Those that do not align themselves with these values are not welcome at Sydney United 58 FC and their views will never be tolerated.
"Multiculturalism and inclusivity are two of the game's fundamental pillars and will continue to be a priority for our club and its supporters."
United hosted the cup final at western Sydney's Commbank Stadium - under FA rules, the home club is "responsible and liable for the conduct of its supporters" with sanctions ranging from reprimands to bans from competition.
