Portuguese prosecutors are investigating the conduct of a policeman who allegedly beat a man in front of his young children and also punched their grandfather outside a football stadium, sparking a national scandal.

The district prosecutor said in a statement late on Monday that it has opened an investigation into alleged abuse of power. The government department that oversees the police also said it is investigating police behaviour at the stadium.

Police approached José Magalhães on Sunday outside the Guimarães stadium, where Benfica had just won the Portuguese league title.

Magalhães said police had allowed him and his two sons, who were wearing Benfica jerseys, to leave the stadium before other fans because the children were being crushed.

Video footage shows the family by a low wall, where one child is sitting and drinking a bottle of water, and a few other people in the vicinity, as police held rival fans inside the stadium to avoid clashes in surrounding streets.

The footage then appears to show an officer questioning Magalhães, then punching his elderly father before using a truncheon to beat Magalhães, who was on the ground, while his nine-year-old child screams “Dad! Dad!”

It appears that Magalhães was struck repeatedly before being handcuffed. Another policeman in riot gear with a shield keeps the child away and then tries to pick him up as he cries.

On Monday, Magalhães told reporters outside a Guimarães court that the policeman asked him why he had taken his children to a football game where he knew there could be trouble. Magalhães said he replied that the police should be more concerned about people getting crushed inside the stadium, at which point he said the policeman assaulted him.

Magalhães said the policeman alleged in evidence presented to the court that Magalhães spat at him – a charge he denied. Magalhães also said the police had been kind to him and his family by allowing them to leave the stadium early.

Benfica said it would invite Magalhães and his sons to watch the final game of the season at its stadium in Lisbon next weekend, and the two children will go onto the field for the presentation of the league trophy.

Meanwhile, the club has criticised some of its fans, who pelted police with bottles and stones during celebrations in Lisbon on Sunday night. Riot police moved in to clear streets after midnight as violence broke out.