"We are not going to speculate on reports from people in the community and we respectfully ask that you wait for the investigation to run its proper course.
"The parents have not been interviewed by the police, this morning arrangements were made for them to be taken to the hospital to be with their baby," she added.
One neighbour, who asked not to be named, described the dog as "docile".
She said she had been into the home "several times" where she saw the dog.
"There was nothing wrong with that dog. It had been around children for a few years.
"Certainly I had no concerns about it," she said.
The woman said Eliza-Mae Mullane's mother had two other children, a boy and a girl both of school and nursery age, and that she had lived at the address for around a decade.
Alaskan Malamutes were originally bred as sled dogs for work in the Arctic, but are now popular as family pets.
The Alaskan Malamute Club of the United Kingdom describes the breed as a "affectionate, friendly, loyal, devoted companion" on its website.
An ideal Alaskan Malamute is "heavily boned, powerfully built", it says.
Alan Lewis, chairman of Pontyberem Community Council, said: "We are only a village of 2,500 to 3,000.
"It is a huge shock for the particular community. Our thoughts go to the family involved, obviously.
"From what I understand, the police are still continuing their investigations and the area is cordoned off."
Mr Lewis described Pontyberem as a "an ex-mining community village".
- UK Independent
