Chairman Dave King says everyone at Rangers "abhors the sectarian element that continues to be so prevalent in Scottish football."
King apologised to Steve Clarke after the Kilmarnock manager said he was subjected to abuse from the "dark ages" during Wednesday's match at Ibrox.
"We will continue to do everything we can at our club to root sectarianism out and to deal in the strongest manner possible with any individuals that are found to have engaged in such practices," said King.
"We are also deeply distressed that Steve Clarke has been subjected to this unwarranted abuse and on behalf of myself and the club, I offer our most sincere apology and hope that it does not deflect him from the wonderful job he has done at Kilmarnock.
"He is a top manager and it would be a great loss to Scottish football if incidents like this forced him away from our game."
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Clarke says "everybody has to take some responsibility" for tackling sectarianism while Killie and former Rangers striker Kris Boyd, who said he experienced sectarian abuse during last week's match with Celtic, insists clubs should not have points deducted for such fan behaviour.
Strict liability is used in Uefa competitions and Scottish clubs have been fined for the behaviour of their supporters in European competitions.
But neither the Scottish Professional Football League nor the Scottish FA adopt such a stance.