The Greenpeace boat Taitu is within 500 metres of the world's biggest seismic blasting ship off the Wairarapa Coast.
The 15-metre launch has been following the ship since last night.
The Amazon Warrior is searching for oil on behalf of Statoil and Chevron.
Greenpeace's executive director in New Zealand, Russel Norman, said he had made contact with the vessel but had not convinced it to stop its operation.
"The captain from the Amazon Warrior has asked us to move away and we've asked him to stop blasting for new oil.
"The facts around this are really straightforward, science tells us that we can't continue afford to burn half of the existing fossil fuel, so it's absolutely completely insane to be out here looking for deep sea oil off the coast of New Zealand if you want a stable climate."
Mr Norman said the Taitu was now within a 500 metre exclusion zone of the Amazon Warrior and they intend to stay close by for as along as the weather allows.