The dog's owner was on a quad bike riding ahead of the dog and did not see the attack.
The council spokeswoman said the owner returned to pull the dog off before letting it go again, at which point the dog returned to attack the pup.
Eventually, the man chained the dog and left the beach, while the pup was seen going back into the ocean.
The council spokeswoman said it was unclear whether the five dead seal pups found on the beach died due to dog attacks or other unknown reasons. However, the council urged people to watch their dogs and keep them on a leash when on the beach.
Pukehina Ratepayers and Resident Association member Leanne Armstrong was shocked to learn of the "dreadful" attack and recent deaths.
"I'm a dog owner too and we are all responsible for our dog's actions on the beach. This attack highlights why dogs must be kept under control at all times and never be left to wander the beach unsupervised."
Armstrong said Pukehina Beach had a growing resident population which led to an increasing number of dogs roaming the beach after being either left home alone or not well-supervised.
The Department of Conservation could not be reached for comment before publication.
All seals are protected under the Marine Mammals Protection Act, and it is an offence to harass disturb, injure or kill marine mammals.
Anyone charged with doing so faces a maximum penalty of two years' prison or a fine of $250,000.
