New Zealand's candidate for the UN top job, Helen Clark, is vowing to stay in the race despite remaining static in the third straw poll.
Portugal's former prime minster Antonio Guterres has again topped the poll for Ban Ki-moon's replacement as Secretary-General, with Miss Clark remaining seventh of the 10 candidates.
Miss Clark's campaign team tweeted after the poll this morning, thanking the UN Security Council and adding "la lucha continua", which is Spanish for "the fight continues".
Prime Minister John Key said Miss Clark had invested a lot in the campaign and should definitely remain in the race.
"This is where it's going to get a little bit more interesting. It looked to us like there was a bit more tactical voting; one of the eastern Europeans has gone up to number two now so you are seeing some change there.
"All of this is really just the preliminary straw poll voting, it doesn't really count until you get to the part where countries, particularly the P5 [five permanent members of the Security Council], start really being able to have significant influence."
New Zealand officials were continuing to advocate for Miss Clark, Mr Key said.
"I'm not disheartened by it, and I think in the very brief text exchange I've had with Helen, I think she is happy that things have stabilised now.
"Look, she's not unrealistic, she's got a hell of a lot of work to do if she's going to get over the line, she's got to start moving back up, but she's got a bit of time to do that."
William Pace is the director of the 1 for 7 Billion campaign, which is pushing for a more open and transparent process to elect the Secretary-General
There remained very strong support for a female to head the UN, and also for regional rotation, he said.
"So I think while former Prime Minister Guterres is clearly the frontrunner in the three straw polls to date, I don't think you can conclude that it's anywhere near over in terms of the final recommendation from the [UN Security] Council on appointment by the General Assembly."
Labour foreign affairs spokesperson David Shearer said Mr Guterres had a great reputation, but because he was from Western Europe and Russia wanted an Eastern European candidate, he might not hang on.
"What has been an interesting in this latest poll is Miroslav Lajcak, who is the Slovakian former foreign minister, who has come from 10th into second, which just goes to show you the degree of which the votes are moving around at the moment."
It is not yet known when the next straw poll will be or whether the next one will be at the stage where coloured ballot papers are used for the permanent five members of the Security Council.
If it does, that will give a clear indication of which candidates could be vetoed by the P5 and the race is likely to narrow at that point.