Prime Minister John Key says a National government would back his predecessor, Helen Clark, if she wishes to contest the position of the next Secretary-General of the United Nations.
Secretary-General Ban Ki-moon is serving his second five-year term, which is due to end in 2016.
The Secretary-General is appointed by the General Assembly on the recommendation of the Security Council and is subject to veto by any of the five permanent members.
Miss Clark is the third most powerful person at the UN, in charge of its Development Programme.
In a recent article in The Guardian newspaper, she leaves her options open when asked whether she would like the top job.
Mr Key says the present government would back her if she does go for the position, although it would be a hotly contested appointment.