A 15-year-old student at a public high school in the New York borough of the Bronx has died of stab wounds.

A 16-year-old boy was taken to hospital for stab wounds in the arm and torso and is currently in "grave condition," according to police. The deceased student had been stabbed in the chest and rushed to St Barnabas Hospital in the Bronx.

Police have said an 18-year-old is in custody under suspicion of being involved in the stabbing at the school complex which includes PS 67 and Urban Assembly High School. All schools in the area were put on lockdown immediately following the incident.

It is unclear at this time if the person in custody is also a student.

A local television news station has reported a "heavy school security presence" around the school complex.

Local police confirmed the stabbings occured at 11 am local time inside the Urban Assembly School for Wildlife Conservation after an argument.

Kevin Sampson, the school’s dean who performed CPR on the deceased student, told the New York Times “it was about what it’s always about, bullying."

Police are questioning the suspect about possibly being bullied and it appears the dispute between the three had been going on for about two weeks.

They had been tossing paper at one another shortly before the stabbing, authorities said.

According to Chief of Detectives Robert Boyce, the 18-year-old walked out into the hallway after stabbing the two younger students.

There, he met a guidance counsellor and handed her a bloodied switchblade.

He then went to the assistant principal's office and quietly sat waiting for the authorities to arrive, Mr Boyce said.

About 15 to 20 other students were in the classroom, but no one else was injured.

The Department of Education has not responded to request for comment.

This branch of the Urban Assembly school has 545 students in grades six through 12. Police reported 11 separate public safety incidents in the first half of 2017.

Public safety reports indicate the school does not have metal detectors students must pass through upon entry, according to the newspaper.

New York City has the country's largest public school system, with one million students.

Chief Joanne Jaffe, head of NYPD's community affairs, said about 75 schools around the district are equipped with metal detectors, and they would do random sweeps of all schools for the time being.

It is the first homicide on New York City school grounds since 2014, when a fight between two 14-year-old boys ended with one stabbed to death outside Intermediate School 117 in the Bronx. The last time someone was killed inside a school was at least 20 years ago.

Mayor Bill de Blasio and Schools Chancellor Carmen Farina said they were saddened by the attack and understood the fear parents would have.

"All of us are feeling this tragedy very personally," said de Mr Blasio.