Several arrests were made during what Police Scotland described as “despicable” and “shameful” scenes at Ibrox Stadium.

Celtic fans initially spilled onto the pitch in celebration after a 4-2 win on penalties in the Scottish Cup quarter-final before Rangers fans also joined the fracas.

Flares were thrown as police and stewards formed a barricade to separate the two groups of supporters.

Chief Superintendent Kate Stephen said the behaviour of several fans “must be condemned by everyone involved in football and wider society”.

She said: “Several 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 disorder quickly settled down with fans returning to the stands as police and stewards formed a barrier between opposing supporters.

It was the first time Celtic supporters were given the full Broomloan Road Stand allocation at Ibrox since it was reduced to fewer than 1,000 in 2018.

Traditionally, around 7,500 Celtic fans filled the stand for Old Firm derbies.

Since then, away ticket allocations at both Ibrox and Celtic Park have fluctuated between about 750 and zero in a series of tit-for-tat moves.

Police said some of the supporters had entered the Broomloan Stand without tickets, forcing delays to the security operation with turnstiles closed for a time.

The Scottish Football Association condemned the supporters who went onto the pitch and said an investigation would be carried out “immediately”.

Scotland’s victims and community safety minister Siobhan Brown, pictured left,  said the scenes were “unacceptable”.

She said: “Of particular concern is the reckless use of pyrotechnics which could have caused serious injury.”

Brown highlighted the fact that the Scottish government had recently consulted on extending powers to ban football fans from games and was “considering next steps”.

Currently, Football Banning Orders (FBOs) are only imposed if supporters are involved in violence or disorder – they enable the authorities to stop fans attending games anywhere in the UK for 10 years.

Both clubs told BBC Sport they would not comment officially yet.

In a post-match interview, Celtic manager Martin O’Neill said: “You’re asking me a lot of political questions in this moment when I’m in a euphoric state.

“The fans have spilled over, big scenes at the end, all over the place. I’m not diminishing it at all; I will think about it and speak to you in due course.”

After the most recent game, where there was more trouble, Rangers and their new manager, Derek McInnes, who was escorted off the pitch by a police officer, refused to make any comment at all.

The latest move from the police and politicians is that Celtic and Rangers have both been ordered to play their next home Scottish Cup match behind closed doors.

That was when Rangers fans charged on to the pitch to confront Celtic supporters who had spilt on to the playing area to celebrate their team’s penalty shoot-out success, but the police at the time described the scenes as “shameful”.

The clubs will now also have to pay their next Scottish Cup opponents £100,000 in compensation for the loss of shared gate receipts.

They have also been warned that any repeat of crowd trouble at Scottish Cup ties in the next two seasons would prompt another closed-door punishment.

Both clubs admitted charges relating to unacceptable conduct from supporters.

An independent review into the scenes previously concluded that “crushing” and “life-threatening violence” were narrowly avoided.

Celtic said the punishment was “disproportionate” following a “relatively small incursion” by its supporters.

A statement from the club said: “Our club has never defended supporters entering the field of play, and we have repeatedly taken action when it occurs.

“However, we understand the part emotion plays in football and would have expected the context and distinction in behaviours to have been taken into account by the panel. Another important distinction is that, on this occasion, Celtic were not the home club, responsible for stadium safety arrangements.

“We will study the panel’s report and reasoning when it is available, and will thereafter consider our next steps.”

Rangers said that the club would “consider the outcome in full, including its implications, before determining any further steps”.

The club also announced that Celtic’s ticket allocation for their Premier Sports Cup quarter-final tie at Ibrox would be just 300.