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Mr Ban is in New Zealand for a two-day visit following a small island development conference in Samoa.
New Zealand is bidding for a seat on the UN Security Council in October.
But Mr Ban said he could not weigh into the issue of whether New Zealand would be successful.
"I'm aware New Zealand is very much enthusiastic to serve on the security council," he said. "As you may appreciate, as the secretary-general I'm not in a position to say anything.
"This is a matter to be decided by the member states.
"At the same time I'm aware of how actively you have been engaging and how actively you have been contributing to issues of international security and development and human rights issues since 1945 [when the UN was founded]."
Asked if New Zealand's moral backing of US airstrikes in Iraq could hinder the bid, he dodged the question, saying: "I hope that this security situation, as it develops, should be discussed more at the security council how the international community can have a more concerted way [of dealing with it], but at the same time when a situation really blows out like this, it's also important to contain the further spread of this political instability and security instability.
"And [because of] that I really appreciate those countries who have the capacity for, and have been addressing, the counter terrorism issues."Mr Ban was speaking at a joint press conference with Prime Minister John Key this morning following a closed-doors meeting.
The pair discussed a "very wide range" of topics, Mr Key said, including Fiji and its upcoming election, conflict in the Middle East, the situation in Ukraine, as well as New Zealand's engagement in areas such as climate change , aid and ratifying the arms trade treaty.
New Zealand was a founding member of the United Nations and Mr Ban praised the country's track record of humanitarian issues.
"It's always a great pleasure to work the New Zealand and New Zealanders," he said.
"Since the beginning of the United Nations in 1945 you have been a champion and an exemplary member state in addressing the three pillars of the United Nations - security, development and human rights.
"When it comes to human rights you are really a champion in upholding gender equality ... That kind of example has been picked up on by member states for seven decades."
My Key also praised New Zealand's "very important role" in the UN.
"We're a small country, but we've held an independent foreign policy and a strong voice for a very, very long period of time," he said.
"We're consistent in what we do and I think people respect the views of New Zealand."
The UN secretary-general last visited New Zealand three years ago.
This weeks short trip will see him receiving an honorary doctorate from Auckland University tomorrow.
Today he will travel to Taupo where he will be shown examples of New Zealand's renewable and sustainable energy efforts.
He praised the country's "strong commitment" to tackling climate change and its consequences, particularly for small Pacific island nations.
"I congratulate your government's very far sighted vision of using more renewable energy, targeting 95 per cent of your energy by 2025, that's quite a big exemplary vision," he said.
"I hope that many member states will emulate this one.
"As I am going to convene a climate change summit meeting on September 23 in New York, I hope a lot of member states, and particularly leaders, will come to New York with a bold and ambitious target so that we can have visions and the political will generated in there."
By Patrice Dougan of APNZ