A soccer fan who gave a Nazi salute at the Australia Cup final in Sydney has been banned for life from any games sanctioned by Football Australia (FA).

FA had promised strong action in response to the behaviour of some supporters in the crowd of 16,000 that watched Macarthur FC beat semi-professional side Sydney United 58 2-0 on Saturday.

Pictures on social media showed some Sydney United supporters making Nazi salutes during the match, drawing condemnation from Australian Jewish groups.

Some fans also chanted and booed during an indigenous Australian welcoming ceremony before kickoff.

"Football Australia  has  concluded  an investigation into the conduct of an identified spectator in attendance at the Australia Cup 2022 final," the FA said in a statement.

"The spectator in question has today been issued with a lifetime ban from attending Football Australia-sanctioned football matches including all NPL, A-Leagues, Australia Cup, and national team matches. The ban is effective immediately."

The statement did not identify the banned individual.

The behaviour of the fans provoked condemnation from New South Wales state Premier Dominic Perrottet, who described it as "absolutely horrendous".

FA said it was collaborating with law enforcement officials to try and identify other fans guilty of anti-social conduct during the match.

Darren Bark, the chief executive of the NSW Jewish Board of Deputies "cautiously" welcomed the ban.

"We look forward to further swift and heavy penalties to be enforced by Football Australia as these fans are identified," he said in a statement to the Australian Associated Press.

"This behaviour was not only an affront to the Jewish community and the Indigenous community but an affront to all Australians."

Sydney United 58 was founded as Sydney Croatia in 1958. Some fans also sang songs associated with the the far-right Ustase movement in Croatia in the 1930s and 1940s.

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