The system “miserably” failed two boys whose drug-addicted mother allegedly drowned one in the Murray River and narrowly failed to kill the other, a lawyer for the family says.

New South Wales Premier Gladys Berejiklian has instructed government agencies to probe their handling of a case, with Dale Brooks, a lawyer for the boys’ grandparents, says authorities were warned of the boys’ “imminent danger” but took no action.

The family is devastated, said Brooks, who told AAP, “they ‘re simply heartbroken.”

Mr Brooks said the grandparents were in a state of shock but rallying behind their older grandson and would demand a coronial inquiry.

“Family and Children Services and Corrections has failed the family miserably,” he said.

It is understood the boys’ grandparents had been engaging with lawyers for some weeks before the tragedy and had raised concerns with authorities.

On Sunday, Premier Berejiklian told reporters it was a “a human tragedy of the highest proportion”.

“We’ve asked for all of our agencies to give us urgent reports on what they knew,” Ms Berejiklian said. “We will be instigating investigations but we will be cooperating with all the authorities to get to the bottom of this.

The father of the boys, who cannot be identified, told News Corp he hadn’t seen his eldest son for six years and had never met the younger brother.

“Now, I’ll never meet him. I don’t want to bury him, he’s meant to bury me,” he said.

The child’s mother has been remanded in custody on a charge of attempted murder.

The investigation comes after New South Wales Police recovered the body of a five-year-old boy from a stretch of river near Moama on Saturday. The body is yet to be formally identified.

The boy’s nine-year-old brother remains in a stable condition in hospital in Melbourne. He reportedly suffered serious dog bites while running from the horrific scene on Thursday afternoon.

The 27-year-old woman, who had only been released from jail a month ago, turned herself in to Echuca police on Thursday night after also suffering dog bites.

She reportedly told witnesses she “had to drown my babies”.

She appeared in a Bendigo Court in Victoria on Friday afternoon with NSW police extraditing her across the border to Deniliquin, where she was arrested and charged with the attempted murder of the nine-year-old.

On Saturday, the woman appeared in Deniliquin Local Court charged with attempted murder in the relation to the injuries sustained by the nine-year-old.

During the court hearing, she was refused bail.

She will reappear, via audio-visual link, at Deniliquin Local Court on Monday. Further charges are expected to be laid at that time.

Brooks said the woman had struggled with an ice addiction for many years and that he had made “considerable representations” to both the Department of Family and Children’s Services and the Department of Corrective Services about the “imminent risk” to the boys.

He said government agencies had “culpability” for what happened to the two boys.

“The mother in this instance has been a really troubled individual, she’s been a long-term ice addict,” Mr Brooks told News Limited.

In a statement, the Department of Corrective Services said it “strongly denies most of the serious allegations against its staff”.

Meanwhile, the older boy’s father has spoken of his devastation to Fairfax Media, saying he was “numb”.

“It’s really hard because I haven’t been in their life for years,” the man said.

“I’m numb, I’m calm, I’m letting the authorities deal with it,” he said, between tears.

Deniliquin police superintendent Paul Condon told reporters the case was “just terrible” and that it “will rock the community of Australia”.

Supt Condon said it was “very unclear” what happened at the riverbank on Thursday evening.

The grandmother said the woman took her car and ”snatched” the children, and then took the boys to a property outside Moama at 4pm on Thursday, where they were fishing in the river.

She allegedly asked the elder boy to get into the river and dunk his head in the water, the court heard.

It is alleged she then held him under the water in an attempt to drown him.

The court was told the boy was able to wriggle free when his younger brother started screaming on the riverbank and the mother turned around.

The older boy was then “savagely mauled” by a dog as he fled the scene.

– with ABC and AAP