They are seeking charges under Section 295 of the Criminal Code and Section 26 (1) of the Child Protection Act, together with Section 78.
The 15 parents were accompanied by Ronnarong Kaewphet, chairman of the Justice-seeking Advocacy Network.
Ronnarong also wants education authorities to look into the licence of the teacher at Sarasas Witaed Ratchaphruek School, who reportedly physically assaulted the kindergartners.
Ronnarong asked the Private Education Promotion Commission to inspect the teaching licence of the accused as her behaviour was unethical.
Police have questioned five parents and sent their children to hospital for medical examination. They are also coordinating with the social development office to ask for details, as the matter is sensitive for the mental health of the children.
As of now, no charges have been pressed against the main accused or the others who are accused of turning a blind eye to the alleged assaults.
Meanwhile, the sacked former teacher on Sunday apologised for her alleged actions, claiming she was stressed about a personal matter and her mother's illness.
The parents of children from other classrooms are also requesting additional CCTV monitoring, as they are worried about their own children and some parents have noted bruises and behavioural changes.
People are now widely criticising the school after footage showed the teacher allegedly abusing a kindergartener, pushing and pulling the student's hair. Her alleged violent behaviour bred fear in children and many did not want to attend school. When parents raised the matter with school authorities, the teacher's aggressive behaviour was reportedly exposed by CCTV footage. She reportedly confessed to the assaults and was sacked.