Police have made nine arrests following the disorder at Sunday’s Scottish Cup quarter-final clash between Rangers and Celtic.

They expect that number to rise “significantly” after launching an operation to address multiple incidents.

Several members of the public and officers were injured after fans invaded the Ibrox Stadium pitch in the immediate aftermath of Celtic’s penalty shootout win over their Glasgow rivals.

Dozens of travelling fans spilled on to the pitch to celebrate and more than 100 Rangers fans charged to confront them.

Police and stewards formed a barrier to prevent large-scale interaction but there was violence and missiles, including a lit flare, were thrown.

Chief Superintendent Emma Croft said that one officer had been hit on the head by a bottle.

Footage also showed a female officer being kicked to the ground from behind by a Rangers fan who was sprinting towards the Broomloan stand, which held 7,500 Celtic supporters.

“There’s nine arrests currently that I can report on. I do expect that number to rise significantly,” she said.

“I’ve mounted an inquiry team and we will go through CCTV and other opportunities to identify individuals who will be brought to justice.

“The biggest concern was injuries to my officers and to members of the public. Three or four members of the public were injured in terms of assaults.

“My officers, the injuries that they suffered were injuries to the head, to the face, to the arm. All violence, all culpable and reckless conduct and disorder. Not acceptable.

“We are aware of a number of individuals that came on to the pitch using items within the stadium as weapons. That will play part of the broader inquiry I’ve kicked off, and we have significant CCTV footage which we’ll be trailing through.”

Police said a 10-year-old child had been hit by a coin.

Television footage showed a man being apprehended by police after an incident involving a member of the Celtic staff, which drew a response from his colleagues, who included at least one player.

Mobile phone footage also showed a fan aim a kick at Celtic defender Julian Araujo, before another ran up and pushed the Mexico international.

Police said a 54-year-old man had been charged in connection with a police assault and a 47-year-old man had been charged in connection with an assault on a coach and player.

Police also had to deal with incidents outside the stadium, including one in which a man was lying injured on Helen Street. Three men, aged 54, 23 and 20, have been arrested and charged in connection with a serious assault.

Footage of an incident in which a female officer was kicked from behind has also been shared widely on social media.

Ms Croft said: “It’s extremely upsetting, and I’m very grateful to say that she didn’t suffer serious injury as a consequence. But hurt, and a pride thing as well I dare say.

“It’s not great to see an officer like that, and in particular on social media to see people celebrate that. That’s pretty hard. Officers go out at the start of the day to do the right thing and keep people safe.”

A review of the police operation has been launched but Ms Croft said she believed enough officers were deployed to police the fixture and she called on clubs to address the behaviour of fan groups.

“My view was we responded as quickly and appropriately as we possibly could at the time,” she said.

“We are dealing with threat and risk in many areas of the stadium, inside and outwith. The public see one area and that’s where the cameras pan to.

“It’s very difficult to respond on the field of play when you have a number of other people who are intent on trying to meet together to cause violence.”

Police are also investigating an incident in which a number of Celtic fans broke into Ibrox before the game, causing a 24-minute delay before supporters with tickets were able to access turnstiles.

Scotland’s First Minister called for a collective approach to tackling the situation.

Speaking to the Press Association on Monday, John Swinney said: “The violence after the Old Firm game yesterday at Ibrox was completely and utterly unacceptable – there is no justification for it whatsoever.

“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.”

He said the use of pyrotechnics “exaggerates and escalates that level of danger”, adding that the Government needs to work with authorities to ensure they are not taken into grounds.