Prime Minister John Key is promoting reform of the United Nations Security Council in support of New Zealand's bid to get on the council in 2015-16.
Mr Key has arrived in New York to attend the UN General Assembly and will use the opportunity to lobby for support.
Mr Key has 18 meetings arranged with other leaders as he tries to win their votes.
Most of them are from small countries as New Zealand argues it can represent their views on the council.
Mr Key says this country has a strong argument to be elected to the Security Council.
It has an independent foreign policy and a proven track record from when it was last on the council in 1993-94.
Mr Key is also arguing for reform of the council, saying the conflict in Syria is an example of the council not working well.
"We've got a situation that's being brokered between Syria and Russia at the moment around the rounding up of chemical weapons but that in part relies on the fact that that job can be done properly and speedily," he says.
"But realistically we think, over the last couple of years, 100,000 people have potentially died in Syria, it's taking an awfully long time for everyone to get involved."
He says the five permanent members of the council should not be able to use or threaten to use their veto when genocide is involved.
Mr Key will also speak to the General Assembly on Thursday and attend a range of other meetings before he leaves on Friday afternoon.
The Prime Minister's staff say he has been suffering from an upset stomach but is carrying on with his meetings in New York.