Fans could have died if police tried to stop the pitch invasion at the Scottish Cup final, according to Police Scotland.

The force have rejected an official complaint about how they handled the match between Rangers and Hibernian that ended in violence in May.

Concerns have been raised about a lack of policing at the match and a failure to control the pitch invasion and subsequent disorder among fans.

In a report commissioned by the Scottish FA, it was suggested there should be a reserve of police available to call on to deal with any trouble, such as that seen on May 21.

In their response to the SFA report said, Police Scotland it would not have been feasible "to have hundreds, if not thousands of officers on standby" just in case a mass pitch invasion took place.

The force added any attempt to halt the pitch invasion could have ended in fans closest to the pitch being crushed by a surge of supporters pushing forward from behind them.

The unnamed author of the police response wrote: "I would point out that, in my opinion, had there been sufficient officers to deter those in the front rows from entering the pitch, any such action could have had a catastrophic effect had the many thousands of fans at the rear of the stadium surged forward.

"In such a scenario, a crushing situation would have been inevitable and could have resulted in serious injuries or fatalities."

The author added: "In the face of thousands of people determined to enter the playing surface, the police and stewards had little or no option into preventing this.

"I can confirm that there were significant numbers of officers deployed to police this event and this was in line with our experience of previous matches."

By the beginning of August, 58 people had been arrested over the violence which followed the Scottish Cup final, which Hibs won 3-2 to lift the trophy for the first time in 114 years.

The SFA report by sheriff principal Edward Bowen QC said both sets of fans were at fault in their behaviour.

He also suggested the government should consider making it a statutory offence to invade a football pitch.

Meanwhile, the Police Scotland response outlines why officers often arrest people after a match when there has been disorder, instead of during it.

The response says: "It is the duty of all police officers to prevent and detect crime and police officers are expected to intervene and arrest persons when it is practicable and safe to do so.

"As such, to make an arrest during a fixture with thousands of supporters within the ground is not always deemed appropriate ... as that can lead to further public disorder."

The response said the invasion came about due to the dramatic ending to the final, with the winning goal coming during injury time.

The response added: "The result of this was a pitch incursion by many thousands of Hibernian fans who were intent on celebrating their club's victory, regardless of the safety rules and laws which are designed to prevent such incursions.

"It is also apparent that amongst the many thousands of fans determined to celebrate, there were a core of undesirable fans intent on 'goading' the Rangers fans and causing trouble."