Celtic and Rangers will attend a summit with Scottish Government and police officials after their stormy cup clash led to questions in the country's parliament.
The Scottish Police Federation repeated their call for the fixture to be banned after opposing coaches Neil Lennon and Ally McCoist clashed on the touchline following Celtic's 1-0 Scottish Cup win, which saw three Rangers players sent off.
Scottish First Minister Alex Salmond confirmed both clubs have agreed to attend a meeting next week to discuss the connection between the game and violence in society.
Salmond added: "In terms of how people's actions have an impact on society, the fans of football matches are representatives of their clubs, the players at football matches are role models for society, and the management of football clubs have a particular responsibility.
"They are people in positions of responsibility and they must - absolutely must - behave responsibly."
Strathclyde Police assistant chief constable Campbell Corrigan had written to Salmond's Government to press for a "frank and open" discussion between all the parties involved.
Thirty-four arrests were made at Celtic Park during the fifth-round replay, for what Strathclyde Police described as a variety of sectarian, racial and breach of the peace offences.
The league match between the teams on February 20 at Celtic Park led to 16 arrests in the ground and more than 229 in the area. In some cases prisoners were said to have been driven 50 miles as police cells filled up.
Mr Corrigan said: "We fully support the clubs and the football authorities in the work that they are doing in addressing many of the problems that affect our society.
"However, the events of the past few weeks have shown that there is much that needs to be done.
"It is the responsibility of us all, not just football, to do everything we can to reduce the violence and end the sectarianism that, sadly, is still ruining lives and is an embarrassment to our country."
SPF chairman Les Gray called for the derby to be played behind closed doors or banned altogether.
He said: "We simply don't have the money and resources to do this. Everyone involved needs to sit down and look at this. Something has to give. This madness cannot go on.
"What happens on the pitch is reproduced throughout Scotland, on the streets, in pubs, in homes. You cannot justify it. It can't keep on going."