"It must be remedied as soon as possible, a task force should be formed to finally take care of things," said Bayern's chairman. "Basically, I am a big proponent of the VAR. It makes the game fairer, but I have the impression that the DFB (German Football Association) should implement professional structures."
The VAR enjoyed a largely successful debut at the World Cup in Russia, but continues to be the source of much debate and disgruntlement in Germany.
The system has just started its second Bundesliga season "and yet does not work as desired," Rummenigge fumed. "It leads to repeated discussions and criticism - the referees are being let down here."
His outburst comes after the VAR stole the limelight for all the wrong reasons.
The VAR was not called into play on Friday after defending champions Bayern were awarded a late penalty, although replays showed Franck Ribery had jumped over a tackle and was not actually brought down in the area.
"Where was the video assistant?" fumed Hoffenheim coach Julian Nagelsmann, but even Bayern's new head coach Niko Kovac admitted he would not have given the penalty.
VAR spurs debate in Bundesliga
Robert Lewandowski eventually converted the subsequent spot-kick in the 3-1 win over Hoffenheim — but only after a delay caused by the VAR insisting the penalty was retaken.
"There is no need for 14 screens in Cologne (where VAR decisions in the Bundesliga are made) - they could stay at home and we'd just have extra screens in the stadium," suggested Nagelsmann. "It would cost less and save all this back and forth."
More VAR-generated chaos followed on Saturday as Schalke, last season's runners-up, crashed 2-1 at Wolfsburg amid unruly second-half scenes.
German stars eager to shine in Bundesliga after World Cup letdown
The video assistant upgraded a yellow card to a red for Schalke defender Matija Nastasic for a bad tackle.
Then three minutes later, he downgraded a red card against Wolfsburg striker Wout Weghorst, who had shoved over a Schalke player.
The two reversals sparked heated exchanges on the sidelines.
Schalke coach Domenico Tedesco claimed he had been "insulted" by match referee Patrick Ittrich, who refuted the allegation, but admitted it had been a difficult afternoon, adding: "You cannot always do everything right."
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