The submission was made before Justice R K Gauba, who was hearing the plea of the girl's mother Sangeeta Gupta, who has refused to believe the suicide theory.
The mother has moved the high court, through her counsel Amit Kumar, following alleged inaction by Delhi Police on her complaint that there was more to her daughter's death than meets the eye.
On the court's intervention, the police submitted that it will lodge an FIR under section 306 (abetment to suicide) of the Indian Penal Code.
The police said that it would carry out the investigation in accordance with the law, on basis of the statement made by the girl's mother.
The Class XII student had left for school at 7 AM on September 16 last year. At about 9 AM, her mother Ms Sangeeta received a call from the school informing her that her daughter had attempted suicide by consuming poison.
Ms Sangeeta's son rushed to the school. A PCR van reached the spot just as he was taking his sister to the hospital on his scooty.
The mother has alleged that the police had not taken any action with regard to a complaint made on April 14 last year about a boy harassing her daughter on the way to school in Azadpur. She had also complained against harassment and abuses over phone from an unknown number.
She has said that she was unable to understand how her daughter could commit suicide when she left home in a normal state of mind. Ms Sangeeta has also questioned how a student can consume poison in a classroom and also write three suicide notes addressed to three different persons.
The petitioner said the authorities concerned had failed to reveal true facts despite repeated requests.
Her counsel has said that neither were the papers of the proceedings shared with the family nor was the CCTV footage of the school obtained to find out the correct cause and manner of death.
The counsel submitted that the police never bothered to look into the complaint regarding the boy harassing her the girl on her way to school, which casts more doubt over the "suicide".
Earlier, the police officials had submitted that they have recovered a suicide note from the bag of the girl, stating "no one should be blamed for her act".