AEK Athens ended a nine-year trophy drought by lifting the Greek Cup on Saturday with a 3-0 win over Atromitos Athinon but their win was overshadowed after dozens of fans clashed with the police following a pitch invasion.
Fans tossed flares, fireworks, seats and plastic bottles on to the pitch following the final whistle and also ripped out advertising hoardings before the police managed to clear the crowds.
"We have asked EPO to change the disciplinary law. If this is not done, the state will suspend all funding to Greek football," deputy culture minister George Nikitiadis told reporters.
"Penalties must be put in place to stop the throwing of firecrackers and for any fan to entering the field of play. These penalties must include the deduction of points and in cases of repeat offending, relegation."
Nikitiadis added that the government would be releasing a new sports bill in June which would enable authorities to hand out stricter penalties to address the problem of violence in Greek stadiums.
Police said 22 officers were injured following Saturday's incident and five of them remained in hospital. Police added 13 arrests were made on charges including possession of explosives, arson, disturbing the peace and breach of the law on extracurricular sport and violence.
Last month, players' union chief Stelios Giannakopoulos said Greek football's image had been "smeared" and needed a major overhaul to rid itself of the crippling problem of crowd violence.
Violence inside and outside stadiums have plagued Greek football this season, endangering the safety of players and fans.
Leading clubs Olympiakos Piraeus, Panathinaikos and PAOK Salonika have been punished with supporter bans after ugly pitch invasions involving battles with police and attacks on players.
"The events of the Greek Cup final once again underline the position of the state that if professional football wishes to maintain its self-governed model, then it must ensure that regulations are followed and that the necessary measures for the smooth organisation of football matches are introduced," secretary for sport Panagiotis Bitsaxis said in a statement.
