"Prevention is critical not just in new conflicts but also in the cases on the agenda where conflict is frozen or where peacebuilding has not really taken hold.
"In Syria and Iraq we see the truly frightening consequences when leadership, both internally and in the Security Council, has failed," Mr McCully said.
"Syria has been a weeping sore for over three years.
"Thousands of Syrians have died; millions have become refugees and all Syrian people have suffered terribly from the multiple conflicts engulfing the country.
"And now the tragedy of Syria has spilled over into Iraq which was already wrestling with its own deep seated problems."
He said New Zealand demonstrated in the past that as a member of the Security Council it acted strongly, effectively, and independently.
"It champions the right of small states and for the voices of all to be heard.
"In short, as my Prime Minister said from this rostrum last year, 'There is no point being on the Council simply to make up the numbers. Sometimes, you have to speak up and shine a light on what is going on - or not going on - even when it is embarrassing or inconvenient to others to do so'."
Mr McCully said that if elected New Zealand would be "a credible, positive influence on the Security Council".
"At our core, New Zealand is an optimistic country and New Zealanders are an optimistic people.
"We believe that things can be better than they are and are prepared, as a people, to work hard to achieve that.
"Despite the many challenges on the international agenda, my hope is that the membership of the UN will give us an opportunity to prove this by serving on the UN Security Council from next year."
Yesterday, Prime Minister John Key said although New Zealand's elite SAS personnel are not yet on standby for deployment to combat Islamic State militants in Iraq or Syria, he would not rule out sending them if asked.
The US State Department has named New Zealand as one of more than 60 countries in the coalition supporting its efforts to counter Isis (Islamic State).
However Mr Key said he had not yet received any requests for assistance.
Asked whether he would send military personnel if requested, Mr Key said: "I can't rule out that there won't be because what you can see around the world is countries being asked to give support."
As far as sending SAS personnel, Mr Key said: "I can't rule that absolutely out, but what I can say is that I'll get advice and we'll see how that goes, but it would be my least preferred option."
The UN Security Council is responsible for the maintenance of international peace and security, its website said.
The council is made up of 15 members. China, France, Russia the United Kingdom and the United States are all permanent members.
The remaining 10 non-permanent members are elected for two year terms by the General Assembly.
