Police Scotland say arrests have been made following the Old Firm pitch invasion and condemned the "despicable display" which ensued at Ibrox after Celtic beat Rangers on penalties in the Scottish Cup quarter-final.
In a Police Scotland statement, it was also confirmed they will work with both Rangers and Celtic in a "robust investigation" which will also include supporters entering the Broomloan Road stand without tickets before kick-off.
Celtic progressed to the semi-finals with a 4-2 shoot-out victory over Rangers after the goalless draw at Ibrox, which sparked a pitch invasion from both sets of supporters.
Missiles were thrown as police and stewards moved to form a barrier between the two sets of fans. Order was then restored as the 7,500 Celtic supporters were left to celebrate alone.
First minister John Swinney has described the scenes as "completely and utterly unacceptable" and says the police have "his full support in pursuing everyone involved in this incident".
Chief Superintendent Kate Stephen said: "The behaviour of a number of supporters at the Scottish Cup quarter-final between Rangers and Celtic at Ibrox today was shameful. It must be condemned by everyone involved in football and wider society.
"A number of arrests have already been made, and Police Scotland will now work with both clubs and the Scottish Football Association to carry out a robust investigation following the scenes on the pitch at the conclusion of the match.
"Officers and stewards were faced with extreme hostility and violence over a sustained period, with many individuals having armed themselves with items clearly intended to cause harm. Officers and members of the public have been injured in this despicable display and I want to express my thanks to all officers and staff deployed.
"The investigation will also include the actions of some supporters who entered the Broomloan Road stand without tickets before the match started, forcing delays in the security operation and the turnstiles to be closed for a period of time.
"I would also urge anyone with information about who was involved in disorder before, during or after the match to get in touch with Police Scotland on 101."
The Scottish FA quickly condemned the fans' behaviour and said "an investigation will be carried out immediately".
"The violence after the Old Firm game yesterday at Ibrox was completely and utterly unacceptable - there is no justification for it whatsoever," Swinney said on Monday.
"There was severe danger applied to fans and to police officers and to stewards, it was completely unacceptable in every respect.
"What I want to make clear is the police have my full support in pursuing everyone involved in this incident, also that we will work constructively with the clubs - who must be horrified by the scenes that they witnessed - as well to address the situation, to work with the Scottish Football Association, to make sure that collaboratively and collectively, we do all that we can to make sure that these types of incidents have no place in Scottish football."
Pyrotechnics were also used by those invading the pitch, which the First Minister said "exaggerates and escalates that level of danger", adding that the Government needs to work with authorities to ensure they are not brought into grounds.
Speaking in his post-match press conference, Rangers boss Danny Röhl said: "I was not on the pitch in the moment; I did not see it until now. I think we all know the emotional situation after a game. Nobody likes to see this.
"It was a great atmosphere for 120 minutes and it should be like this; the other things should not be in the stadium or in football."
Celtic players were escorted off the pitch as the chaos ensued, with manager Martin O'Neill providing further details after the game.
"It's a big derby game and I think there was a lot of jubilation at us winning. The fans spilt over and I suppose it is very difficult to quell that," O'Neill said.
"As we were making our way back, there was some kind of fracas and someone had tried to get on the field. It's unfortunate [scenes at the end] but hopefully it doesn't dilute the performance in terms of character.
"All I saw was a bit of a scrum down at the bottom. As you say, maybe it does taint proceedings but I think there was an element of self-protection in that one.
"I am making judgments on things I only half saw. From my viewpoint, it was a great win for us. Rangers are very strong and had the full week to go at it."
On whether the pitch invasion from supporters would overshadow the victory, O'Neill added: "That would be a worry for me.
"The fixture itself, although still a phenomenal fixture, had lost a bit of its lustre because the away fans or the full complement of away fans were not allowed in.
"I have no idea what might happen. I think today, with the crowd and our crowd there, to me, it was a proper Old Firm game in that sense. We will see what develops."
Former Scotland international Charlie Adam labelled the pitch invasion a "disgrace" and said both sets of supporters let themselves down at Ibrox.
"It's a disgrace," he said on talkSPORT. "It's a sad day for Scottish football.
"For the Old Firm that we talk about being our leadership teams and [what] they represent, it's an embarrassment for our game.
"And as a national team we're trying to improve and we're trying to get better. But these two clubs have let us down as a nation and they have to have a look at themselves today.
"Both football clubs have to look at themselves because they are the standard-bearers for us as football clubs and they have, both [sets of] supporters have let themselves down.
"It's an embarrassment for Scottish football. This should not be happening. In this day and age this should not be happening and we have to get control of it quickly because if it doesn't it'll keep escalating and escalating and there'll be big, big problems."
