Nakira Griner is accused of the killing. [Photo, Courtesy]

A mother who told police her toddler son had been kidnapped is now accused of dismembering the child and incinerating his remains.

It's also been alleged that she carried some of little Daniel Griner Jr's body in her handbag by police in New Jersey.

According to the Vineland Daily Journal Nakira Griner, 24, has been charged first-degree murder; second-degree endangering the welfare of a child; second-degree desecration of human remains; and fourth-degree tampering with evidence.

Court paper released on Monday say the burned and dismembered remains of 23-month-old Daniel were found in a handbag and trash bags underneath a shed at the family's home on Woodland Drive early Saturday.

Police told the local paper that Griner had initially reported she was attacked Friday evening while walking with Daniel Jr. on the 200 block of Atlantic Street.

Griner said she had her other child, an infant son, strapped to her chest.

Daniel Jr. was in his pushchair, she had told police.

At the time, the paper said a complaint filed by Detective Veronica Cappoli states: "She stated she felt someone kick her; she fell to the ground and was repeatedly kicked on her right side and head. Nakira said when she looked up the stroller with D.G. Jr. was missing.

"Nakira was not able to provide any descriptions of the accused or her route she ran after the attack."

Further questioning revealed inconsistencies in her story, the newspaper said.

Her home was searched and remains identified as human were found about 3am Saturday.

The mum later failed a polygraph examination with New Jersey State Police.

The affidavit Cappoli filed states that Nakira Griner admitted during the examination to having hurt her older son.

The paper said Coppoli stated the Nakira Griner said she left bruises on the boy's face and that he also had fallen down stairs.

"She told police she hit the boy because he would not eat or listen to her, according to the report.

"She then said that she left D.G. Jr., who was still alive, by himself on Devonshire Place because she wanted someone to find him and help him because no one would believe her," Cappoli stated.

The police investigation is continuing.