Derry City and Bohemians have issued a joint statement condemning those involved in trouble outside the Ryan McBride Brandywell Stadium on Friday.
The PSNI said that rival groups attacked one another with weapons, with two people taken to hospital, and damage to property reported. No arrests were made.
Videos posted online showed clashes, including a commercial firework being fired horizontally by one group.
The clubs statement said that those involved in the trouble had "no interest in supporting either team" and that their actions "put the safety of genuine supporters at serious risk."
Further, the clubs intend to work with the FAI to "agree a way forward that protects all who attend our games and maintains the long-standing and valued relationship between both clubs."
The action inside the stadium ended in a 1-1 draw as Dipo Akinyemi put the Candystripes ahead in the first half before Ross Tierney equalised after the break.
Derry City FC and Bohemian FC joint statement, in full: "Derry City FC and Bohemian FC, on and off the field, from board level right down to our respective fanbases, have enjoyed a fantastic relationship down through the years.
"Both clubs are committed to working together to do everything in our power to protect and strengthen that relationship into the future.
"It is therefore with great regret to both clubs that incidents, before and after our game at the Ryan McBride Brandywell Stadium on Friday night, from individuals with no interest in supporting either team, put the safety of genuine supporters at serious risk.
"The safety of everyone - supporters, players and staff - is, and will always be, of paramount importance to both clubs.
"For Derry City FC's part, the club has been working tirelessly over the last couple of days with our match night security team to establish the circumstances surrounding the disturbances and to reassess the procedures in place for travelling supporters.
"Both clubs have also been working in tandem with the FAI to agree a way forward that protects all who attend our games and maintains the long-standing and valued relationship between both clubs.
"All parties are very much aware that this is an ongoing investigation. That process must be respected, and therefore neither club will be making any further comment."
