Mr McCully and Mr Kerry have worked closely together on oceans diplomacy already with their joint bid to create a 1.34 million sq km marine reserve on part of the Ross Sea, which they will again promote at the 25-member Commission for the Conservation of Antarctic Marine Living Resources this year.
On his way to Iran, Mr McCully will visit Turkey, a rival to New Zealand and Spain for a seat on the Security Council.
He said he had made a point of maintaining good relations with both rivals, and visited Spain this year.
New Zealand was co-operating closely with Turkey on the 100-year commemorations at Gallipoli next year.
"We simply can't let Security Council competition get in the way of an important relationship."
Iran has been the subject of UN sanctions over its enrichment of uranium and the extreme anti-Western rhetoric of former President Mahmoud Ahmadinejad kept it isolated as well.
Mr McCully's visit to Iran comes on the back of greater engagement by the West after talks led by the EU foreign policy chief Baroness Catherine Ashton to curb its nuclear development in return for easing of sanctions.
Commenting on his trip to Iran next weekend, Mr McCully said the ruling regime had been more constructive than their predecessors.
He would mention New Zealand's bid for a seat on the Security Council but it was not a lobbying trip.
Mr McCully said there had not been an active boycott of Iran by New Zealand.
For the past five years New Zealand had decided not to take part in the political and economic consultations that were meant to occur every two years but had not joined in the non-UN sanctions imposed by others such as the US and Australia.
