New Zealand Law
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You can do this although I do suggest you have a discussion with the neighbour and try to sort this out amicably first. If that is not possible you will need to send a fencing notice under the Fencing Act which specifies the type of fence. You will likely also need the council to consent to the proposed fence and depending on the nature of the fence, a resource consent
Under section 8 of the Fencing Act a fence cannot encroach without either consent or a court order. The act says
Fence not to encroach without consent or court order
(1)Notwithstanding anything in this Act, no person is entitled to erect a fence that encroaches to any degree whatever upon any land of which he is not the occupier, except—
(a)with the consent of the occupier of that land; or
(b)pursuant to an order of the court made under section 24.
(2)Where any fence erected otherwise than in accordance with subsection (1) encroaches upon any land of which the person who erected the fence is not the occupier, the occupier of that land may apply to the court for an order that the fence be removed; and the court shall order the removal of the fence (at the expense of the person who erected it) unless it is satisfied—
(a)that the degree of encroachment is minimal; and
(b)that the encroachment in no way adversely affects the use and enjoyment of his land by the applicant.
So you can tell the neighbour that they either agree, or you will apply to court and get this sorted, in accord with the section cited above