The visitor also complained that Savvidis attacked AEK director Vasilis Dimitriadis. AEK said it will file a complaint with Federation Internationale de Football Association and UEFA, the world and European soccer governing bodies.
"More relevant announcements to be made shortly".
AEK's Spanish manager Manolo Jiminez told Spanish radio that Savvidis went straight to the referee, showed him his gun and said: "your career as a referee has ended".
The first time he was wearing an overcoat, and AEK Athens officials claimed that Savvidis threatened a referee.
The Greek Deputy Culture Minister for Sports Giorgos Vasileiadis said: "Images of team owners invading the pitch armed are setting back soccer for years".
A victory for PAOK would have seen them narrow the gap on AEK at the top of the Greek Superleague table so the explosive reaction from home fans at Toumba Stadium hardly came as a surprise.
Earlier Sunday the Greek FA's appeals committee annulled a decision to dock three points from PAOK over the February 25 match with Olympiakos that was called off before kick-off after visiting coach Oscar Garcia was hit by an object thrown from the stands.
"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".
"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.
Olympiakos itself is appealing a decision that had deducted three points from the team for fan behaviour in a February 4 home game against AEK, which it lost 2-1.
Lille have won the Ligue 1 three times, having won the last title in 2011, and are now one place off the bottom of the table.