The Prime Minister says he will continue to push for Helen Clark to become the next United Nations Secretary-General, despite her coming eighth out of 10 in the latest poll.
Miss Clark dropped one place from the previous poll, but received fewer discourage votes from the 15 Security Council members.
In statement Miss Clark said she was pleased with her improvement among a tight pack of candidates and would continue with her campaign.
John Key said he had had a brief text conversation the former Prime Minister, who was pleased with her latest numbers.
He said there was still a long way to go and lots of high-level discussions to be had before the final decision was made.
"We're very much in those early stages, there's a lot of work to be done, there's some candidates in front of her that are still polling very, very well.
"But we'll just keep pushing that case when we're in New York in about 10 days time and that'll be the opportunity to continue to have discussions."
Foreign Affairs Minister Murray McCully said there were many high-level negotiations still to be had but he said Miss Clark was absolutely justified to keep campaigning for the job.
"This is the word the Prime Minister was receiving in Vientiane, I've been getting separately, particularly in New York, countries want to have her on that short-list, so that when the serious negotiation starts she's one of the options on the table."
Labour Party foreign affairs spokesperson David Shearer said there was still plenty of horse trading left to do before a new United Nations Secretary-General was named.
He said the world leaders week coming up later this month at the UN would be a key moment for Miss Clark's campaign.
Mr Shearer said Miss Clark would be looking to talk to the leaders to get an indication from them.
"It'll also be obviously dependent on, where the permanent five go, because the votes aren't all equal on the Security Council, the permanent five members if they have a discourage vote or an anti vote it's effectively a veto."
Former Portuguese Prime Minister Antonio Guterres remains the frontrunner with 12 encourage, two discourage and one no opinion.
Clark's position precarious - RNZ correspondent
RNZ's United Nations correspondent Nick Harper said the result was not what she would be expecting at this stage of the contest.
He said Miss Clark is in a precarious position but the UN General Assembly is just a week away which would provide an opportunity for her to do some intense lobbying.
There was still a chance that some of the higher place candidates could be excluded from the race if one of the permanent members of the Security Council vetoed them, Mr Harper said.
That would still give Miss Clark the opportunity to come from behind and it would be a good idea for her to stay in the race, he said.
In the third poll on 30 August, Miss Clark received eight 'discourage' votes, putting her in seventh place, and the runner-up of the previous race for the position said that suggested she should pull out.
She came seventh in the second poll as well, with six 'encourage', eight 'discourage', and one 'no opinion', having dropped from sixth in the first poll.
Russia has been pushing hard for a Secretary General from Eastern Europe, arguing it is its turn. It is rumoured the Russians have shown strong opposition to Mr Guterres, which could open the way for another candidate.
There have been three Secretary-Generals from Western Europe, two each from Asia and Africa, and one from Latin America, but none from Eastern Europe.
The Secretary-General is approved by the General Assembly on the recommendation of the Security Council.
The next straw poll will be held on Monday 26 September (New York time).