The parents of a six-day-old baby girl thought to have been killed by the family dog have said they will "cherish the little time" they had with her.
Eliza-Mae Mullane was airlifted to the University of Wales Hospital in Cardiff yesterday after what is thought to have been an attack by the family's Alaskan malamute dog.
In a statement, her parents, Sharon John and Patrick Mullane, said: "Even though she was an important part of our family for such a short period of time, Eliza-Mae will always be in our hearts and thoughts and we will cherish the little time we were able to share with her.
"She was a dearly loved daughter, sister, granddaughter and niece.
"She brought joy into our family, and losing her like this has cast the most horrible shadow over all of us. There are no words we can use to describe what we feel at the moment, and we don't think there ever will be.
"We are extremely grateful for all the support shown to us by the community. We are now trying as a family to come to terms with what's happened, and ask that we are allowed to do this in privacy. Thank you."
It is "very unlikely" that there will be any updates on the police investigation until the end of the week, a spokeswoman for Dyfed Powys Police said.
A post-mortem examination is not expected to be carried out until then.
The dog is still alive, and the spokeswoman said: "We've still got the dog, and no, it hasn't been destroyed at the moment."
The parents have not been interviewed by police, she added.
The force has not confirmed whether the animal was responsible for the death, or the type of injuries sustained by Eliza-Mae.
Neighbour Patricia Punter, 70, has been widely reported as overhearing the baby's mother screaming: "The dog ate my baby's head."
Police were called to New Road, Pontyberem, Carmarthenshire, Mid Wales, at 8.30am yesterday, when officers s eized the dog.
Alaskan malamutes are not listed under the Dangerous Dogs Act and police have said the invest igations are still at an early stage.
A police spokeswoman said yesterday: "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."
Chief Inspector Ieuan Matthews said: "The baby girl was just six days old.
"Clearly, our sympathies are with the family at this tragic time and we have specialist officers who are supporting them. All I would ask is that you give them time and space to grieve.
"As far as our inquiries are concerned, the investigation is still at an early stage."
One neighbour, who asked not to be named, described the dog as "docile".
She said: "I have been into Sharon's house several times and the dog - it was like a husky - has been there, it doesn't cause any harm.
"There was nothing wrong with that dog. It had been around children for a few years. Certainly I had no concerns about it."
The woman said the victim's mother had two other children, a boy and a girl of school and nursery age.
Ms John has lived at the address for around decade, the neighbour said.
Mr Matthews said: "It's a real tragic incident and we are at the early stages of investigating.
"Our hearts, as individuals and as a police service, go out to the family, parents and the wider community. We have got specially trained family liaison officers supporting the family through this very difficult time.
"The little girl is six days old, tragically. As you can imagine, the family are hugely distressed. These are tragic circumstances and our hearts go out to everyone involved."
Rebecca Evans, Labour Assembly Member for Mid and West Wales, spoke of her sadness at the tragedy.
"I am shocked and saddened by what I am reading about the tragic death of a baby girl in Pontyberem today. My thoughts are with the family," she tweeted.
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 an "affectionate, friendly, loyal, devoted companion" on its website.
An ideal Alaskan malamute is "heavily boned, powerfully built", it says.
The death comes barely a week after 11-month-old Ava-Jayne Corless was killed by a dog as she slept.
The girl was in bed at a house in Blackburn last Monday when she was savaged by a pit bull terrier.
The girl's mother Chloe King, 20, and her partner, Lee Wright, 26, were held on suspicion of manslaughter and subsequently bailed.