A man has died after being shot by police opposite a primary school in Sydney's south-west.

Just before 9:00am AEDT, four officers were called to a home in Wangee Road at Lakemba after reports a man was trying to hurt himself.

They say when they got there the 36-year-old had stabbed himself.

His father, aged 65, was at home.

Assistant Commissioner Stuart Wilkins said the officers found the man lying on the ground but he then moved, threatening police.

"We believe he has grabbed a knife from the kitchen and confronted police," he said.

A sergeant, with 21 years of experience in the force, reacted by shooting him.

The man was taken to Canterbury Hospital in a critical condition but later died.

It is not yet known if he died from a bullet or a self-inflicted stab wound.

Assistant Commissioner Wilkins said the policewoman did have a taser but he does not know why she did not use it.

He says she is being counselled at Campsie Police Station and an internal investigation is underway.

One neighbour told the ABC he was shocked by the shooting.

"As you can see there is a school opposite, mothers dropping off kids; [the street] has been very quiet," he said.

The New South Wales Government rolled out tasers to frontline officers last year, promoting their importance as an alternative weapon to a gun for police dealing with the mentally ill.