POLICE have described their response to fan trouble at the Scottish Cup final as "measured, proportionate and professional" as separate probes into the disturbance were confirmed.

Police Scotland said a full criminal investigation into the scenes that marred the end of the game between Rangers and Hibernian is under way, and warned that further arrests are likely in the days to come.

Meanwhile, the Scottish Football Association (SFA) has announced it plans to set up an independent commission to investigate the circumstances that led to the crowd trouble at Hampden Park, Glasgow.

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READ MORE: Scottish FA set up Independent Commission to probe Hampden riots

Hibs have issued a statement condemning the violence on Saturday and said the club will do all it can to support the criminal investigation.

Rangers said players and staff were assaulted as thousands of Hibs supporters flooded on to the pitch following the Edinburgh team's dramatic 3-2 win at Hampden.

Fans of the Glasgow team also made it past stewards on to the pitch, leading to a period of fighting between the two sets of supporters before mounted Police Scotland officers restored order at the national stadium.

So far 11 arrests have been made and police are trawling through CCTV and online footage of the trouble to identify those involved.

Assistant Chief Constable Mark Williams said: "A full criminal investigation is now under way.

"We have a dedicated incident room established in Glasgow and I'd appeal to anyone who has information in relation to criminal behaviour at Hampden on Saturday to contact detectives on 0141 532 5457.

"Although we've made 11 arrests so far, I fully expect more to be made in the coming days as we sift through evidence from CCTV and other video footage and photographic images.

READ MORE: Hibs pledge to do "everything in its power" to find those involved in Hampden violence

"Public safety is our number one priority and the pitch incursion was unacceptable and jeopardised that. Our response was immediate, measured, proportionate and professional. In a short period of time, we deployed mounted officers, public order and conventional officers to separate the opposing supporters."

He added that it is important to reflect on the match and work with the other organisations involved to see if there are any lessons to be learned.

SFA chief executive Stewart Regan said after the match that the incident was an embarrassment to Scottish football.

He has promised swift action with the governing body's compliance officer set to launch his own investigation while the independent commission looks into the causes.

In a statement, Mr Regan said: "I would urge all parties involved in the ongoing situation to demonstrate calmness, clarity of thought and responsibility as we proceed towards a satisfactory conclusion.''

The win marked Hibs' first Scottish Cup triumph since 1902. On Sunday, thousands of jubilant fans cheered players as they held aloft the trophy on a parade through Edinburgh.

The club said on Monday it is sorry that a number of supporters invaded the pitch and stressed that it will "co-operate fully with all of the relevant authorities to identify supporters involved in behaviour which tarnishes the good name of Hibernian FC".

HeraldScotland: Police attempt to push back the Hibernian fans at Hampden

Chairman Rod Petrie said: "It is now clear from various sources that supporters being on the pitch at the end of the match led to acts of violence and disorder.

"I condemn and the club condemns all of the violence and unacceptable conduct perpetrated on the pitch and elsewhere and in the margins of the match at Hampden. There is absolutely no place for it in the game of football.

"Hibernian will do all that it can to support the criminal investigations to ensure that those who have transgressed face the consequences of their actions."

READ MORE: Scottish FA set up Independent Commission to probe Hampden riots

One steward was slightly injured but security group G4S said staff did a "good job considering the situation".

The general secretary of the Scottish Police Federation praised the "professional" response of officers.

Calum Steele said it is hard to prevent pitch invasions when thousands of people take part.

He told BBC Radio Scotland: "In their own right they are not a precursor to violence. Recent experience in England has shown that they are a significant display of joy and elation but on this occasion that joy and elation that was enjoyed by many, many thousands was marred by the activities of, I suspect, a few hundred."