The mother of two boys found dead in the Blue Mountains had been sacked from a government department on mental health grounds.
The bodies of two boys - Russell, aged 11, and Ben Smith, nine, were found at their Faulconbridge family home on Tuesday.
Police are waiting to question their 42-year-old mother after she was taken from the scene to hospital with minor injuries.
NSW Premier Chris Minns confirmed reports the mother had previously been sacked from a government department job due to mental health issues.
"The information I've been given so far is ...the employee was let go from a NSW government agency," Mr Minns said on Friday.
"It was challenged in the Industrial Relations Commission, the original decision of the government department was upheld, and I believe it was handled appropriately."
The mother's personal Facebook page is filled with photos of her and the children together, showing them on frequent bushwalks and beach visits.
She and the boys' father Nick were separated.
Russell and Ben Smith were 'happy, outgoing boys, very much loved by their family and friends'. (HANDOUT/NSW POLICE)
Investigators have declined to speculate on what occurred before the brothers were killed but police have said they are not looking for any other parties.
The premier said government departments would cooperate with any of the "major inquiries" he forecast into the tragedy.
"Both from the homicide squad and the NSW Police as well as potentially the Coroner's Court as well," Mr Minns said.
"If new information comes to light, of course government agencies and the NSW government will supply that to any independent investigation that takes place, this is a very serious alleged crime."
In a statement on Thursday, Mr Smith expressed his disbelief at the tragedy while also calling for privacy.
"The loss of our two beautiful boys has caused unimaginable pain and distress," he said.
"Russell and Ben were happy, funny, outgoing boys and were very much loved by their family and friends."
Mr Smith, who does not live at the Blue Mountains home, found the boys about 1pm on Tuesday and contacted police.
Their mother was taken to hospital in a stable condition. She has not been charged.