SYDNEY (AFP) - The Australian police said on Tuesday a woman and three children aged under 10 have been found dead, apparently from gunshot wounds, in a rural farmhouse, and they are searching a man aged in his 40s.

Police in New South Wales state said they went to the house in the small town of Lockhart, 535km south-west of Sydney, at 3pm and found the bodies in the house. The Daily Telegraph newspaper said the victims were a mother and her three children.

"While they have not yet been formally identified, they are believed to be a woman, aged in her 40s, two girls and a boy, aged 10 and under," the police said in a statement late on Tuesday. "While a post mortem will be conducted to formally establish the cause of their deaths, they are believed to have all suffered gunshot wounds."

Police said they were still searching the property and had "grave concerns" for a man aged in his 40s, who "remains unaccounted for".

Lockhart Mayor Peter Yates told regional newspaper The Daily Advertiser the deaths had "devastated the community".

"We're all saddened by it, of course... I know the family, they're a well-respected farming family and it's just so devastating.

"I just can't believe it... especially when there's children involved, they had their whole lives ahead of them."

Lockhart is located in a farming region and has a population of just over 3,000 people.