"One of the most important considerations for countries sorting out who they are going to vote for is to think they are going to have a fair-minded and constructive country so that if anything relating to their interests or their region comes on to the agenda, they can feel confident that countries on the council are approachable, ready to listen and are constructive in the way they respond."
It was particularly important in Africa because African issues dominated the Security Council agenda.
He said that through functions such as the Waitangi Day function, he wanted to make it clear that "New Zealand is not just a 'little England', that we are a country with a strong indigenous and Pasifika personality and we have our own way of arriving at conclusions on international issues".
Mr McCully will also attend the New York launch of the African Union Handbook, after attending the launch with African Union ministers last week in Addis Ababa, Ethiopia.
The launch was "an opportunity for me to rub shoulders with the leadership of AU and to make a speech at a gathering of 400 or so leaders of the AU".
Mr McCully said it was important to keep up the pace on the campaign for the Security Council.
Security council bid
•NZ's rivals are Spain and Turkey
•Vote will be held in mid-October
•The seat is for 2015 and 2016