Outrage over a children's "fight club" has led to a court appearance for three teenagers, prompting calls for a legislation change to target the behaviour.

Two boys and a girl have been reported by police who are searching for four other teens after videos posted on social media showed children fighting in Adelaide parks.

Almost 40 other children may be involved in the "fight club" after being spotted in the videos, South Australia Police Commissioner Grant Stevens said.

The online footage allegedly shows children grouped in weight classes in pre-arranged fights in parks across Adelaide.

Fight videos have reportedly been posted for months but came to light this week, prompting an "absolutely appalled" Premier Peter Malinauskas to take time out of his holidays and condemn the behaviour.

"It is completely unsafe and perpetuates raw violence in a way that cannot be tolerated, particularly amongst children," Mr Malinauskas posted.

"Our kids should be taught how to respect one another, rather than violence to be displayed on social media."

The three teens were reported for fighting in public after the premier asked the state's attorney-general and police minister to "crack down on this behaviour".

Two boys - aged 14 and 17 - were initially reported before a 13-year-old girl was located by police on Wednesday.

They will be summonsed to appear in court at a later date, police said.

"Police have identified another four boys involved in the incidents and are attempting to locate them."

Another 36 children could allegedly be seen in the fight videos posted online but had not yet been identified, Commissioner Stevens said.

The top cop had been asked by Police Minister Michael Brown to look at potential law changes if fight club organisers could not be charged under "posting and boasting" legislation.

"We'll have a look at whether or not there are opportunities for enhancing legislation that makes it more difficult for people to organise these types of events or activities or to participate," Commissioner Stevens told 891 ABC Adelaide.

Attorney-General Kyam Maher confirmed current laws were being examined after being "shocked" by the fight club allegations.

"In SA, boxing and martial arts events are strictly regulated. Real harm can happen when there aren't strong measures in place around these activities," he posted on social media.

"We are actively examining current laws, specifically those relating to boxing and martial arts, and if we need to strengthen the laws to better protect kids, that's exactly what we'll do."