A schoolboy who killed a senior teacher calmly accepted a suspension for driving on an athletics field hours before he opened fire with his policeman father's gun.

Robert Butler went home to speak with to father and some friends, giving no hint of the horror to come.

But after his father left to run errands, Butler, 17, took his service handgun from a cupboard and headed back to Millard South High School in Omaha, Nebraska, to confront the administrator who had punished him.

Butler, whose father is a detective for the Omaha Police Department, asked to see assistant principal Vicki Kaspar and shot her in her office. He then wounded principal Curtis Case and fled before killing himself. Ms Kaspar, 58, died in hospital hours later.

Police outlined the events that led up to the shooting, which unfolded at the school on the first day of class after the Christmas break.

Butler had transferred to Omaha in autumn from a school in Lincoln, about 50 miles away. On New Year's Day he had been cited for criminal trespassing after driving his car on the school's football field and track.

Butler was called out of class at 8.10am on Wednesday to see Ms Kaspar. The two talked in her office and he was escorted out of the school at 9.23am.

But Butler had remained calm after learning of the suspension.

"He wasn't acting like an out-of-control student at all," police chief Alex Hayes said. The teenager received a ride home, where he talked to his father and spoke to some friends by phone.

Butler's parents decided to transfer him to Omaha because he was having disciplinary problems in Lincoln and had not been listening to his mother, who is divorced from his father, Mr Hayes said.

Butler's father had no any reason to expect his son would turn violent because he did not seem distraught about the suspension and had no history of mental illness.

"He was disappointed with the discipline, but he wasn't acting angry," Mr Hayes said.

District schools superintendent Keith Lutz paid tribute to Ms Kaspar, describing her as a dedicated professional.

Butler's father left home for about 40 minutes and it was then that his son took his father's handgun out of a cupboard, posted an ominous message on Facebook predicting he would do "evil things", and broke into a locked garage where his father had stored his car since the trespassing incident.

"When we, as police officers, leave our houses, we do not expect our children to commit crimes like this," Mr Hayes said.

Butler returned to the school at 12.45pm, but still did not seem upset and even signed in at the administrative office, asking to see Ms Kaspar again.

"He walked into the school just like a normal student. He was not displaying any firearm or weapons," Mr Hayes said.

Police said he was in her office for about four minutes with the door closed before he shot her. Butler then walked across a hallway and shot Mr Case, 45.

Butler also fired at a custodian and missed and debris hit a school nurse, who was not seriously hurt.

An unarmed security officer sitting at a desk outside the school's main offices saw Butler walking away. Butler pointed a gun at the officer, who took cover and was not shot.

A school resource officer who heard the gunfire called police.

The security officer gave police Butler's name and described his car and at 1.35pm, authorities received a report of a suspicious vehicle about a mile from the school.

Officers raced to the car and found Butler inside, dead from a self-inflicted gunshot wound.

The gun was his father's service weapon, a .40-calibre semi-automatic pistol that can fire up to 15 rounds. Butler fired seven rounds.

After word of the shooting spread, panicked pupils took shelter in the school's kitchen and in locked classrooms while police checked the building.

Mr Case was in a serious but stable condition in hospital and had been able to speak to family members, Mr Lutz said.

School classes were due to resume today.

Butler's rambling message on Facebook described his unhappiness with the school but did not supply many details.

He wrote that the Omaha school was worse than his previous one and that the new city had changed him.

He apologised and said he wanted people to remember him for who he was before affecting "the lives of the families I ruined". The post ended with "goodbye".