The bodies were found in Sydney's southwest after a call to triple zero from the home shortly before 8pm on Monday, police said.
Officers entered the Campbelltown home and found the bodies of two boys, aged four and 12, and a 46-year-old woman inside.
A 47-year-old man was arrested, refused bail and appeared briefly at Campbelltown Local Court on Tuesday.
"My client is pretty distressed at the moment," the man's lawyer Jawad Hosain told reporters outside the courthouse.
"It's obviously a tragic set of circumstances for the victims, the community and the family of the victims and he's pretty distraught."
The man did not apply for bail in court.
The matter was adjourned to July.
Police believed the three victims were the arrested man's wife and children, Acting Superintendent Michael Moroney said.
He said police had no prior knowledge of domestic violence incidents at the home.
"Whilst I can't give you specific information in regards to how they passed, what I can tell you is that all three persons sustained significant injuries and it was a particularly violent crime scene," Supt Moroney told ABC News on Tuesday.
"What this does is really highlight the scourge that domestic violence is across society."
The alleged murders follow a four-day blitz on known domestic violence offenders by NSW Police that resulted in nearly 1000 arrests.
Between Wednesday and Saturday, 993 people were arrested and 2063 charges were laid, with 299 arrest warrants executed.
Police also seized 94 guns and 48 other weapons during Operation Amarok.
NSW's prison population recently hit all-time highs under the weight of increasing domestic violence charges, with more than 14,000 imprisoned.
Almost half of all people in custody are on remand, with 41 per cent of this increase attributed to those charged with domestic and family violence.
This can be compared to 14 per cent charged with sexual violence, 13 per cent for non-domestic violence assault, and 10 per cent for weapons offences.
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