An Irish woman living in Australia is in critical condition after she was shot at a house in the Northern Territory city of Darwin.

The Irish Independent is reporting that the woman, aged in her 30s,  is originally from Co Mayo and is the mother of a young child.

It's understood that she is a social worker.

Her name has not been released, and her family have been informed.

She was found with severe abdominal injuries at the property.

The suspected shooter, a 35-year-old man, was later pronounced dead at the scene and it is believed he took his own life.

Media reports in Australia say the local police do not anticipate the need to make any arrests.

Police were called to the home, in Milner in the northern suburbs of Darwin at 6.30 pm on Tuesday after reports of gunshots.

First responders managed to stabilise the woman who underwent surgery on Tuesday night and remains in a critical condition.

Northern Territory Police Detective Senior Sergeant Paul Morrissey said yesterday, police and emergency services were called to an address in Sprigg Street in Millner at 6.30 pm "for a report of two people suffering gunshot injuries”.

"At the location, first responders identified a female and 35-year-old male, both with apparent gunshot injuries," he said.

"The female was conveyed to Royal Darwin Hospital, where she remains in a critical condition in the intensive care unit.

"The male was declared deceased at the scene."

Sergeant Morrissey said: "Firearms have been located, and there does not appear to be any danger to the public.”