The bodies of the boys, aged nine and 11, were found about 1pm on Tuesday at a home in Faulconbridge, west of Sydney.
Their mother, who was found injured inside the home with their bodies, was expected to be questioned by police on Wednesday.
Investigators have declined to speculate on what occurred before the brothers died but they are not looking for any other parties.
The mother, 42, spent the night under arrest in hospital, where she was earlier taken in a stable condition. She has not been charged.
Police have declined to speculate on what had occurred before the young brothers died. (Dan Himbrechts/AAP PHOTOS)
The boys' father, who does not live at the Blue Mountains home, found the boys and contacted police.
The mother's personal Facebook page is filled with photos of her and the children smiling together, showing them on frequent bush walks and beach visits.
The brothers attended school on Monday and police are investigating their movements since then.
Premier Chris Minns said the "horrifying, very distressing" incident was another reminder of how difficult the job of emergency services could be.
"I can only imagine what the father of those two boys is going through today and I want to assure him the people of NSW are behind him as he deals with the turning of his life upside down," he told reporters on Wednesday.
"(This) has obviously distressed the people of NSW and I want to assure them every help will be provided to the father of those two boys in the days ahead as he deals with this incredibly distressing situation."
Blue Mountains mayor Mark Greenhill said the loss of "two precious souls in the most awful circumstances" would affect the entire community.
"Now is a time to come together and remember these two beautiful children and their extended family whose grief must be unimaginable," he said on social media.
Police Commissioner Karen Webb and Superintendent John Nelson addressed the media. (Dan Himbrechts/AAP PHOTOS)
NSW Police Commissioner Karen Webb attended the local police station to provide support to her officers, noting many had children the same age as the boys.
Clinicians and support officers were on hand for police, while the boys' father was also receiving support.
"The older and more experienced you get in this job, things like this still cut to the core," Ms Webb said.
"It's a tragic situation and certainly ... more will be known as the investigation unfolds."
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