"I have just been re-elected as a constituency member of Parliament and unlike list members who can leave without triggering byelections, I am not in that situation so I have never had any intention other than to see the full term."
He said he did not know where the rumours came from.
"But I can only imagine that people may perhaps have been misled by the level of interest I showed in the UN Security Council campaign and have seen some personal ambitions behind it but that is not the case."
Mr McCully is expected to make many trips to the United Nations during New Zealand's tenure on the Security Council which began on January 1.
He and Prime Minister John Key are likely to chair some council meetings during July when it will be New Zealand's turn to take the chair.
New Zealand's ambassador is Jim McLay, a former deputy prime minister and former National leader.