Prime Minister John Key says the results of the latest UN poll vindicate Helen Clark's decision to stay in the race to become Secretary General.
The straw poll overnight puts Clark in eighth place out of 10 - one place lower than the previous two polls.
The former Prime Minister and current UN Development Programme head was given six "encourage", seven "discourage" and two "no opinion" votes.
In the only positive sign, in the third poll she had six "encourage", eight "discourage" and one "no opinion".
Her office said the result was a pleasing improvement.
Key said Clark would be "naturally pleased" that her position had improved slightly.
"I think it would probably vindicate her decision to stay in the race because her main argument has been there's a long way to run yet."
Key said it was early stages and there was still a lot of work to be done.
"There are some candidates ahead of her who are still polling very, very well, but we'll just keep pushing that case for her in New York."
Asked if the change in vote was due to the US, Key said it was impossible to know.
The established frontrunner, former Portuguese Prime Minister Antonio Guterres, came out on top again in the poll overnight.
The vote could swing drastically in the final days with the Security Council's permanent members - the US, Russia, China, France and Britain - holding vetoes that could strike Guterres and other favourites out.
Russia has been lobbying strongly for an eastern European candidate, while other nations, including the US, are believed to be pushing for the next UN secretary-general to be a woman.
In the first poll Clark came sixth and in the second and third polls she fell to seventh.
With the drop to eighth, she trails Guterres, Slovakia's Foreign Minister Miroslav Lajcak in second place, former Serbian foreign minister Vuk Jeremic in third, former Macedonian foreign minister Srgjan Kerim in fourth, Unesco director-general Irina Bokova of Bulgaria fifth, former Slovenian president Danilo Turk sixth and Argentinian Foreign Minister Susana Malcorra in seventh.
A fifth Security Council vote will be held on September 26, with the plan to recommend a consensus candidate to the 193-member UN General Assembly in October.
Clark has said it's a tight pack and she intends carrying on with her campaign.
Voice of America's UN correspondent Margaret Besheer said Clark began as a strong candidate, but for some reason wasn't succeeding in the polls.
"She's just not really resonated with the council members and she's been solidly in the middle of the pack and now she's just dropped down to the bottom."
Foreign Minister Murray McCully said the signals both he and Key had been given was that Security Council members wanted Clark to remain an option on the shortlist once the vetoes came into play.
He said in the past all Eastern European contenders had been vetoed out when it was Eastern Europe's turn.
"It is important to have people like Helen Clark available if we do get to that point."
While that might not happen this time he was certain some of the candidates above Clark would fall.
"When you look through the list this time it is very easy to see many of those who fare better than Helen Clark through the straw polls are going to go the way of the veto. So if we look at a net list of candidates for the short list, I think she's in reasonable shape and is justified in making the decision to stay in the contest."
The straw polls are held in secrecy and while the overall results have been leaked there is no indication of the way individual Security Council members have voted.
That will become clear in October when the first ballot with coloured papers is held - including which candidates will be vetoed by permanent five members of the Security Council: China, France, Russia, the United Kingdom and United States.
The straw poll held on September 26 is straight after Key's visit to New York for leaders' week at the UN General Assembly.