Many of the leaders' speeches at the General Assembly have voiced a belief that the Security Council must give some teeth to the Russian proposal that Syria hand over its chemical weapons.
United States media reported yesterday that the draft terms of a possible resolution had almost been hammered out among the five permanent Security Council members and was likely to be presented to the rest of the council today.
Mr Key said there was little question a seat on the Security Council would give New Zealand a lot of influence in such cases, as it had dealing with Rwanda when last on the council in 1993.
He had discussed the matter with former Prime Minister Helen Clark - now a top UN official - in a private meeting yesterday, and she said New Zealand's bid could succeed, despite rivals Spain and Turkey being much larger countries.
"New Zealand is seen as a good country around the UN. It doesn't have enemies. It's seen as constructive and engaged, so there's always a lot of warmth for New Zealand."
His tactic for securing support appears to be targeting the smaller countries - the reasons were clear in East Timorese President Taur Matan's address yesterday which publicly backed New Zealand, saying: "We believe she will both enhance the voice of small states and be a constructive bridge builder at the council."
Mr Key also met Palestinian President Mahmoud Abbas in New York, and said he offered any help New Zealand could provide with the Middle East peace process. New Zealand had supported greater recognition of Palestine by the UN when it was recognised as an observer at the General Assembly last year. Palestine's bid to be upgraded to a non-member state is on hold while the Middle East peace process is under way - US Secretary of State John Kerry had set a deadline of April to achieve that.
Mr Key offered Mr Abbas any support New Zealand could give.
"They were very grateful for the way we supported them in the UN recently. It's a nine-month process, as he explained to us, the clock is ticking. But the will and determination to get something done is there. We've been at that place before and it's failed. But you do get the sense, that they want to find a way through."
Meanwhile, Fiji's interim Prime Minister, Frank Bainimarama, likened his 2008 coup to historic events such as the French Revolution and American Civil War in his UN address. He criticised Fiji's "old friends" for turning their backs on the island nation.
Commodore Bainimarama said many stable democracies were forged from turbulent events such as the French Revolution, Australia's Eureka Stockade and the US Civil War.
"All nations struggle ... to overcome their unique challenges, to correct historic sins; we are no different."
He said that despite this, Fiji's "old friends" had "turned their backs on us" and imposed sanctions. He also made it clear that it was China to which Fiji now turned.
"Our isolation led us to seek out new relationships that have proven fruitful. Now, our standing in the world has never been stronger."
New Zealand recently loosened its sanctions and provided resources for elections after Fiji's leader pledged to hold them in 2014. Mr Key will not have a meeting with the commodore while at the UN.
