"However we do need people to be safe about it and we have had several near-misses on the motorway already today."
"So please, if you are out and about for a bit of whale-watching today, head to a designated parking spot before getting out of the car."
The presence of the whale has caused tonight's Matariki fireworks display to be delayed until next week, because the show could cause the whale to behave unpredictably - harming itself or people out on the water.
Some online commentators say the whale's presence is a more appropriate celebration of the Matariki festival than a fireworks display.
Although it has been delighting onlookers, the whale has been causing a bit of trouble for the Interislander ferry, which has had to delay berthing on some occasions.
A Facebook page called Matariki the Wellington Whale is running a competition asking people to send in drawings of the whale to win a supermarket voucher.