The dog was found in Derry’s Ballyarnett Country Park on Wednesday, March 15.
Local SDLP Councillor Brian Tierney said: “What kind of person would drop bricks on the skull of a poor helpless dog?
“Then crush the ribs in to collapse the lungs and then to bury it alive?
“Ballyarnett is a lovely place and is often crowded with young children.
“We don’t need or want this in our community.”
The police have appealed for information in relation to two men seen in the area at the time.
The dog suffered suspected brain damage, broken ribs and suspected collapsed lungs before being put to sleep, a Derry dog charity said.
Vivian Kelly, who works for Pet FBI, said it was the worst case of animal cruelty she had ever seen.
Ms Kelly said the dog, an American bulldog called Luna, was found by a member of the public and taken to a vet where it was determined its injuries were too severe.
The dog later “peacefully passed away in the arms of a volunteer”, Ms Kelly added.
“The entire team here are just devastated – completely devastated and still shook up by the whole thing.”
She described the incident as “soul-destroying” and questioned how anyone “could inflict such cruelty on a defenceless animal”.
‘Sickening and shocking act’
The Police Service of Northern Ireland (PSNI) said it was aware of the “level of concern and anger in relation to this absolutely sickening and shocking act”.
Ballyarnett neighbourhood Inspector Ryan Robb said officers had been to the country park and conducted checks of the location where the dog was found.
The police said they have also been checking CCTV in the area, speaking to residents and conducting house-to-house inquiries.
The PSNI appealed for anyone who may have been in the park and saw what happened, or anyone who knows who is responsible, to contact them.
They also appealed for information on the two men seen at the park.
One of the men was said to have been wearing a distinctive camouflage hooded top with the hood pulled up and the other was described as having a slim build with black hair and wearing a dark blue tracksuit.
Anyone with information about the two men is asked to contact police on the 101 number.
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