A NSW mother accused of attempting to drown her two young sons in the Murray River on the NSW-Victoria border allegedly told witnesses she "had to drown my babies".

Her 9-year-old son is in hospital after suffering serious dog bites in the incident on Thursday evening, while his 5-year-old brother is missing, feared drowned in the river near Moama.

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

Police said there had been "a couple of incidents" involving the family since she was released, while the boys' grandmother had feared her daughter was a risk to her sons.

Advertisement

The woman appeared in a Bendigo Court in Victoria yesterday afternoon with NSW police extraditing her across the border to Deniliquin, where she'll be formally arrested and charged with the attempted murder of the 9-year-old.

NSW Police said further charges would depend on the result of the search for the 5-year-old.

Fairfax Media reports that the woman appeared via video-link in court where a detective said she'd "made full admissions to her role in the incident and told police of her 'intention to kill' both children".

The court also heard she had allegedly told witnesses she "had to drown my babies".

AAP understands that the children had been living with their grandmother for more than a year.

The grandmother's lawyer, Dale Brooks, said he had made "considerable representations" to both Family and Children's Services and Corrective Services about the "imminent risk" to the boys.

The daughter was taken to the grandmother's home when she was released from prison, he said.

"The help she was after really was she wanted her daughter moved [away]," Brooks told AAP yesterday.

"They are saying they couldn't find somewhere."

The lawyer said the mother had struggled with an addiction to the drug ice for many years.

Marine rescue NSW search the Murray River for a missing boy in Moama, NSW. Photo / News Corp
Marine rescue NSW search the Murray River for a missing boy in Moama, NSW. Photo / News Corp

"It's an appallingly sad country town saga," he said.

The grandmother claims the children were "snatched" and she holds NSW corrections and police responsible.

The mother had been in prison for "several serious offences", NSW Police Superintendent Paul Condon said yesterday.

AAP understands those included breaking and entering.

Condon said it was "very unclear" what happened at the riverbank on Thursday evening.

"I think this will rock the community of Australia," he said during an emotional press conference.

"The dog has been involved. The dog has bitten the 27-year-old mother and the 9-year-old. The actual circumstances are unknown."

It is thought the dog might have been trying to help the 9-year-old.

Asked if the mother could subsequently also be charged with murder, Condon said: "I don't know. It depends what the result of the search is."

Police hope the 5-year-old will be found alive and around 30 searchers from the Rural Fire Service, the SES, and Victorian and NSW police have combed the riverbank while police divers searched the water.

The mother knows the owners of a property at Moama where the 9-year-old was found with serious injuries on Thursday evening.

The two boys have different fathers and police are working to locate the men.

- AAP