The incident took place just after 3pm on Wednesday.
The NSRI spokesperson, Craig Lambinon said the City of Cape Town (CoCT) Marine Animal Stranding Network was immediately alerted to the incident.
He said officials from the Department of Environment, Forestry and Fisheries (DEFF), NSRI Melkbosstrand rescue swimmers, SPCA Wildlife Inspectorate, and CoCT authorities responded.
Members of the public also assisted on the scene.
“Two pygmy sperm whales, a juvenile and an adult beached in shallow waters on the beach at Slabber se Klippe, Melkbosstrand. Extensive efforts to return the whales to sea appears to have resulted in the adult returning to sea and authorities are cautiously optimistic that the adult whale, appearing to be healthy, will survive,” Lambinon said.
He said the juvenile whale beached again in the vicinity of the NSRI Melkbosstrand slipway.
Rescue swimmers, assisted by public volunteers, tried extensively to return the whale to sea.
“After all efforts were exhausted, the decision was made by DEFF, in cooperation with the SPCA and City officials, to euthanise the whale humanely to prevent the whale from enduring suffering,” Lambinon said.
Gregg Oelofse, of the CoCT Marine Animal Stranding Network, said the decision to humanely euthanise the animal is made in accordance with the approved marine animal stranding protocols, in a coordinated decision made by DEFF marine scientists, in cooperation with the SPCA and City of Cape Town authorities.
“After the extensive efforts, that are commended, by NSRI and by public volunteers, to return the animal to sea, the decision made to prevent the animal from enduring any further suffering is humane,” Lambinon said.