The incident occurred at Banksia Road Public School at 9.45am.

The two boys, both aged eight, were taken in a critical condition to Westmead Children's Hospital, where they were pronounced dead.

They were among five patients taken to the hospital after the crash, a NSW Ambulance spokesperson said.

Two eight-year-old girls were taken to hospital in a stable condition and one nine-year-old was transported in a serious condition.

A further 17 children had been assessed at the scene as well as one adult, the female teacher.

Police said the driver of the Toyota Kluger was a 52-year-old woman.

Acting Assistant Commissioner Stuart Smith said they did not believe the incident was intentional.

"We're not looking this as an intentional act. It is a crash investigation," he said. 

"We're working with forensic services group, we're methodically working through the circumstances of this crash. We have a 52-year-old local woman who is with police at this time. She's cooperating with blood and urine testing and the processes that accompany that investigation."

"This is a horrific, you know, this is a horrific incident for all."

A spokesman for the NSW Education Department, meanwhile, confirmed the weatherboard school building that housed the classroom contained asbestos.

"While asbestos containing materials have been identified inside the building, the removal of any asbestos that may have been disturbed in the damaged building will be managed in compliance with SafeWork NSW requirements," he said.

Khaled Arnaout was one of the first responders on the scene and said it was chaos.

"I heard a loud bang but I didn't take much notice of it. I was just about to hop into the car to get going and then I heard kids screaming. My daughter goes to that school. I ran across the road there was a big hole in the building. Teachers and everyone were just running around. There was blood and kids on the floor, just lying down and screaming.

He said he was assisted by others in lifting the car off one of the trapped children. 

"Someone said 'There's someone stuck under the car, help us.' We lifted up the car straight away and just got him. We ran him to the office and straight away got him into CPR and put him in the recovery position. He was pretty bad, he had a big gash on his head. I kept doing CPR until [the ambulance] got there. They kept asking for the defib and there was no defib there. It might have made a big difference if there was a defib there.

"The driver was in shock. I actually felt sorry for her but I couldn't give her any attention. I just left her there."

NSW Ambulance Superintendent Stephanie Radnidge said ambulance officers arrived to "a scene of carnage". 

"[There were] a number of distressed and overwhelmed children and teachers at a scene of a horrible accident.

"Obviously they were crying, they were distressed, some were asking for their parents, that's a natural response in such a terrible set of circumstances.

"It is very, very hard because we are parents ourselves, we are human beings.

"To those persons who have assisted in this terrible tragedy prior to paramedics arriving, of course the families, paramedics and everyone involved want to say thank you for going above and beyond for caring to those people in that terrible time of adversity."

Year 4 student Mariam Issmail was in a classroom nearby and said everyone in the class was very scared.

"We were just doing our work and all of a sudden we just heard this big bang," she said.

"We were crying. Kids were screaming and saying I want my mum, I want people, I want help. We had to stay in the classroom and stay until our parents came."

Her mother Khadije said that she was shocked when she first heard the news.

"My neighbour told me. I couldn't even speak."

Police are urging anyone with information in relation to this incident to call Crime Stoppers on 1800 333 000​.