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Greenpeace is calling on the Government to turn around the Amazon Warrior, which arrived in New Zealand waters today to search for oil on behalf of Austrian company OMV.
Ardern, who during the election campaign said climate change was her generation's nuclear free moment, said it had become clear that the Government is legally bound by "some quite strict criteria".
"The question for us now is, is that criteria fit for purpose.
"We are bound by the Crown Minerals Act. That sets out some quite strict criteria on which we can make a decision. Much stricter than I would have thought would be reasonable.
"I think it is only fair that we now look at whether that legislation is fit for purpose."
Greenpeace climate campaigner Kate Simcock told TV 1 that the Taranaki Basin was a feeding ground for blue whales, and she understood the Amazon Warrior was proposing three months of seismic blasting.
"The impacts on blue whales in this area are likely to be torturous, interfering with their communication and feeding."
Energy and Resources Minister Megan Woods said she expected a decision to be made "very soon" on whether a permit would be granted.
"There are set of criteria the decision is made on under the Crown Minerals Act…there is nothing around what broader concerns there may be environmentally or otherwise.
"This obviously remains something our Government would need to look at for future decisions to see if this is the right kind of set of questions that we should be asking when we are making decisions like this."