Rangers say they will do "everything possible" to stamp out the type of abuse aimed at Kilmarnock boss Steve Clarke in Wednesday's Scottish Cup tie.
Clarke said he faced "sectarian" abuse from the "dark ages" at Ibrox as his side lost 5-0 in their last-16 replay.
The Scottish FA says it will seek further discussions with government and police in light of recent incidents.
Rangers said the club "wishes to make it clear that unacceptable behaviour will not be tolerated at Ibrox".
They added: "Everything possible will be done to eradicate this kind of behaviour."
Clarke said he was called "a Fenian b******" at Ibrox, three days after Kilmarnock's former Rangers striker, Kris Boyd, said he was subjected to sectarian abuse and was hit by a coin during Sunday's Premiership game with Celtic at Rugby Park.
A statement from Kilmarnock said their board and "everyone at the club is fully behind Steve in condemning sectarianism in all its forms".
"There is no place for sectarianism in football or society," it added. "We are an inclusive family club, who celebrate the diversity of our staff, players and supporters."
Kilmarnock director Cathy Jamieson had earlier tweeted it was "time to end this nonsense once and for all".
SFA chief executive Ian Maxwell said the parent body "condemns in the strongest possible terms the spate of incidents this season involving unacceptable conduct in Scottish football".
"This season we have witnessed match officials and players hit by coins, sectarian singing at matches and abusive and threatening behaviour towards match officials, players, managers and coaching staff," he said.
"Football has a responsibility to take action. We must do all that we can under our current rules and engage with clubs to seek to eradicate such behaviour.
"This issue, however, is not one that football can solve on its own."
He said that he, along with Scottish Professional Football League counterpart Neil Doncaster had met Cabinet Secretary for Justice Humza Yousaf, Minister for Public Health, Sport and Wellbeing Joe Fitzpatrick and Police Scotland assistant chief constable Bernie Higgins to discuss the matter and "will seek further discussions in light of the most recent events to maintain the momentum for change".
'It is difficult to combat if you don't throw a punch'
Wednesday's incidents at Ibrox are the latest to blight the Scottish game this season.
Former Celtic and Hibernian boss Neil Lennon said he was "fed up of laughing off racism" after he was hit by a coin during an Edinburgh derby last October.
David Scott, Campaign Director for anti-sectarian charity Nil by Mouth, believes Scottish football "has failed for generations to tackle sectarian abuse".
"It is difficult to combat if you don't throw a punch," he told BBC Radio Scotland.
"The vast majority of people who go to matches have no truck with this, they just want to enjoy the game. The problem is this noisy, sizeable majority who are dragging us back to the bile and hatred of the old days.
"The dilemma for the silent majority is how you actually deal with the people within your ranks who are behaving in this manner? The clubs, particularly the Old Firm clubs, invest hundreds of thousands of pounds on sophisticated software and CCTV footage where you can identify people.
"But what we have is a reluctance to pursue this. There can be hundreds of people - whole stands - chanting and police can't wade in and make arrests.
"So we are brought back to the elephant in football's room, which is 'strict liability'."
|What is strict liability?
|"Uefa uses a system called 'strict liability' to tackle offensive behaviour at matches. Under strict liability rules, a club is responsible for the conduct of its fans regardless of whether the club itself is to blame. Sanctions include warnings, fines, annulment of the result of a match, order that a match be replayed, the closure of sections of grounds, playing matches behind closed doors and the docking of points."
Scottish clubs rejected a move to introduce strict liability in 2013.
"What we have seen, particularly from the Old Firm clubs, is a complete washing of hands where they say 'this is nothing to do with us, this is society's problem, we can't solve it'," Scott added.
"You would not behave like that in the workplace or in the community without sanction, so why do we allow this permissive environment? It is simply because the clubs and governing bodies don't have the backbone, the bottle, the spine to do something about it."
'How we stop it I don't know'
Hearts manager Craig Levein said "every manager gets abuse" and believes the incidents at matches are part of "a society problem".
"How we stop it I don't know," he added. "The problem with strict liability is if you want to mess around and cause trouble if you are a supporter of another club, you buy tickets for your nearest rival and shout sectarian abuse. Then you get the club fined.
"So what's to stop that? I think it's a really difficult situation to deal with. I think the clubs need to do everything they can.
"I know that we have had difficulties in the past. Clubs need to do everything they can to find them and try to ban them. That's the only way we can do it."
'We have got a cancer and we need to stamp it out' - analysis
Former Scotland midfielder Michael Stewart on BBC Sportscene:
"Steve Clarke is a man of integrity and he shouldn't have to listen to it. But it is very difficult to police it because what happens if a whole stand is shouting sectarian abuse?
"If clubs are serious about stamping it out, for me strict liability is the only way we are going to get to the root cause of the issue. I know it is turkeys voting for Christmas but ultimately the prize is much bigger.
"This is a great country we have got here but we have got a cancer and we need to stamp it out."