Supporters from Celtic and Rangers had organised pre-arranged access to Hampden Park before Ultras clashed outside the stadium today.
Police said early arrangements had been made for fans to set up displays, with Celtic supporters due to gain access on Saturday and Rangers on Sunday morning.
Cops issued the statement after video footage was posted on social media earlier today showing a huge rammy between rival fans outside at around 9am.
The supporters, who were mostly dressed in black, began shouting and chasing each other near the burger stalls as they came to blows.
Traffic cones could be seen being thrown as a number of police officers tried to control the melee.
Punches were thrown between the sets of supporters as one person hit the floor before appearing to be kicked by a number of others.
Cops praised officers for dealing with the 'situation' and preventing it from escalating.
A statement from Chief Superintendent Mark Sutherland, Divisional Commander for Greater Glasgow, following the Scottish League Cup final between Rangers and Celtic at Hampden:
“Prior to today’s match supporters of both clubs had been granted pre-arranged access to Hampden Park by the stadium operators to set up displays, with Celtic on Saturday, 25 February and Rangers on the morning of Sunday, 26 February.
“A stewarding and policing plan was in place to support this arrangement. At around 8.50am on Sunday, 26 February, during this pre-arranged attendance, a disturbance took place outside the stadium involving supporters from both clubs.
“I commend the work of our officers who acted swiftly in challenging circumstances to prevent escalation and disperse those that were intent on disorder.
“No arrests could be made at the time and we will now be investigating the circumstances, I would expect the footballing authorities and both clubs will do likewise and take appropriate action."
Four other arrests were made today for disorder-related offences and one assault.
Chief Superintendent Sutherland added: “After the match police intervened or responded to a small number of incidents, including Victoria Road, which were quickly resolved.
“Only 4 arrests were made for disorder related offences and assault and I would like to thank the vast majority of supporters in attendance.
“Our policing operation continues this evening with a proportionate plan to keep people safe.”
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