The mayor of a town where a woman and her three young children have been found shot dead says the local community is in severe shock.

"It's a devastating time for our community," Peter Yates, the mayor of Lockhart in the NSW Riverina district, told ABC radio on Wednesday.

The victims are a 41-year-old mother, her son, aged 10, and two daughters, eight and six.

Mr Yates said the family was community-minded and well known in Lockhart, which has a population of 900, and locals were "severely in shock" after learning of their fate.


"It's just really, really, really traumatising," he said.

Mr Yates said the council was considering bringing in special counsellors to help the community deal with their grief.

Police found the bodies of the children inside a house on Boree Creek Road, northwest of the town, on Tuesday afternoon.

The mother's body was found on a path at the back of the home.

A post-mortem examination is still to be conducted, but police say it's believed they all died from gun-shot wounds.

Officers are searching for a man, 44, who's missing from the main home, and have focused on a dam at the property after an unattended white utility vehicle was found nearby.

Forensic officers worked through the night examining two crime scenes set up at the property's homestead and at the dam.

Police divers will search the dam and other waterways on Wednesday.

The man is described as Caucasian, about 193cm tall, with a medium and athletic build, short brown hair and clean-shaven face.

Police have urged the public not to approach him and contact officers immediately if he is seen.