Although Savvidis reportedly has a licence for his revolver, he is wanted by police for entering the playing area, police sources told AFP.
The Greek-Russian businessman marched on to the pitch armed with the firearm after a disputed goal.
Savvidis defended his behaviour.
“Ivan (Savvidis) didn’t threaten anybody with a gun,” his media department told Russia’s Sport Express newspaper.
“It means that the provocative headlines in certain media are totally untrue.
“He carries weapons as he has a permission for it. It’s not prohibited in Greece.”
The match was suspended in the 90th minute after PAOK defender Fernando Varela’s goal was initially ruled offside, prompting an angry protest from the hosts that led AEK to walk off the pitch.
AEK had complained that Savvidis came on to the pitch with a gun in his hip holster and threatened referee Giorgos Kominos, who was reportedly told “you are finished” by PAOK technical director Lubos Michel.
Kominos some three hours later changed his decision and awarded the goal to PAOK – if the 1-0 scoreline stands they would take over first place in the Greek table from AEK.
The referee could not convince AEK to return to complete the final few minutes after they expressed concern for their safety.
The visitors also complained that Savvidis attacked AEK director Vasilis Dimitriadis.
Savvidis had asked his team to leave the pitch in protest after Kominos’s decision, but PAOK’s Portuguese captain Vieirinha refused and the team did not go to the locker rooms, unlike AEK.
Savvidis’ press office told Sports Express: “PAOK are currently in the (Greek league) leading group with fair chances to win the title.
“It has caused various provocations against the club. Savvidis has allowed himself some excessive emotions but, once again, he didn’t threaten anybody with a gun.”
Greek media reported Monday that the leftist government is seriously considering suspending Super League contests until judicial authorities clear up pending decisions on matches involving violence.
Deputy Sports Minister Giorgos Vasiliadis is scheduled to meet with Prime Minister Alexis Tsipras and measures are certain to be announced.
“There is no need to talk, but to take tough measures,” Interior Minister Panos Skourletis told Athens News Agency.
“The scenes that we have seen have hurt Greek football. Anyone who comes on the pitch with a revolver is provocatively unacceptable.”
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