"Project Jonah provided logistical support and assistance," the post reads.
Currently, the whale's cause of death is unknown. In November last year a stranded orca was successfully refloated on the same beach.
Meanwhile, a whale expert has told Newstalk ZB that Wellington's visiting southern right whale could be coming into the harbour because it's pregnant.
NIWA marine ecologist Kim Goetz says if it's a female, it may have chosen Wellington harbour to give birth.
"They do come into shallower water to have a calf, it is the time of year where that could potentially happen."
She says it's hard to estimate how much longer the whale will stay around for, because no one knows why it's here.
"If it was sick it probably would have stranded by now. It could be trying to head north and maybe took a wrong turn."
The whale has been attracted a lot of attention last week and even resulted in acting Mayor Jill Day postponing the Matariki Sky Show.
