Greece has faced an unusually volatile league championship this season, with traditionally dominant Olympiakos - which has only failed to win the title twice in the past 21 years - now in third place, behind leader AEK and PAOK.
According to Reuters, the gun was holstered around Savvides waist, and he was surrounded by bodyguards.
Savvidis entered the field of play with his gun in the holster and threatened the referee prompting the AEK Athens players to leave the field.
With the score at 0-0, PAOK had a goal ruled out for offside in the 89th minute.
The match was abandoned two hours after the incident. When the decision was made, fans launched onto the pitch to complain and Savvidis wasn't far behind.
His deputy minister for sport, Yiorgos Vassiliadis, had earlier told reporters after an emergency meeting with Tsipras that the Superleague championship would "not start again without a new framework agreed by all".
Club president invades pitch with gun
Games were suspended in all divisions after referee's chief Giorgos Bikas was the victim of an arson attack in November 2016, while investigations into a match-fixing scandal that came to light in 2011 remain ongoing.
"We did not worry to begin with but afterwards when you see the gun you think 'if he was going to do something insane he could have taken it out".
Savvidis, a Greek-Russian tycoon who used to be a member of the Russian parliament, took to the field twice, followed by his personal security.
"We will not allow to anyone to derive us from our target even if we need to take tough decisions in communication with the UEFA".
"The scenes that we have seen have hurt Greek football".
"West Ham United have immediately launched a full and thorough investigation into the incidents which marred the second half of today's match and are committed to taking decisive and appropriate action", said a club statement on Saturday.
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