No one was arrested when police were forced to come between groups of protesters in George Square yesterday.
And a top cop has admitted "known football risk groups" have been identified on both sides.
Chief Superintendent Alan Murray says a review will of the shocking scenes will take place, warning that action will be taken against those breaking the law.
He spoke out after clashes between rival protesters claiming to be 'guarding' city centre statues, the Daily Record reports.
He said: "A sizeable number of individuals identified as being from various groups gathered in George Square this morning with a stated intention of protecting statues.
"Throughout the day, police officers were required to intervene due to the presence of opposing groups to maintain order and public safety.
"Both factions included known football risk groups.
"There have been no arrests in connection with the event."
A mass rally had initially been set up to call for the removal of the statue of former Prime Minster and founder of the Metropolitan Police Sir Robert Peel by the Glasgow Youth Art Collective - which was later cancelled.
But another group urged its supporters to watch over it and hundreds descended on George Square today.
Missiles were thrown between two groups and cops in riot gear had to separate the sides.
Chief Superintendent Murray added: "As is usual with events of this nature, a review will take place and should any criminality be identified appropriate action will be taken."
Earlier, Nicola Sturgeon branded the violent clashes as "utterly shameful".
At her daily coronavirus press briefing, she pointed out: "Violent protest is never acceptable.
"I say to anyone that has found themselves on the streets of Glasgow in an altercation with other groups or with the police, that they should really take a long hard look at themselves.
"That is not acceptable behaviour at any time, but at this time of crisis that the country faces, I think it's particularly shameful behaviour."
