A man has been found dead after carrying out the "premeditated" shooting murders of his two children in Australia, police have said.

The bodies of a girl, 13, and a boy, 15, were discovered in their bedrooms in Sydney on Thursday.

Police found the 68-year-old man's body in a home in a nearby suburb on Friday.

The children's mother was not at home when they died, police said, adding that she was later treated for shock after arriving at the scene.

"I cannot imagine the significant stress and heartache she is going through," said Assistant Commissioner Brett McFadden from New South Wales Police.

"Nothing can prepare you to walk into a home and see two children in that state. There [are] no words that we can say to the family."

Police said the man had been involved in a custody dispute. He had not been living at the children's house in the suburb of West Pennant Hills.

"This [shooting] is something that has been premeditated and planned," Mr McFadden said.

Two handguns believed to have been used in the killings had been recovered, police added.

Australia has strong gun control laws, introduced after a mass shooting 1996, but individuals can register to own firearms.

Children who are killed by their parents or caregivers account for 18% of family-related murder cases in Australia, according to the most recent government figures.