Helen Clark remains in seventh place in the third straw poll of the UN Secretary-General race.
In the second straw poll earlier this month Miss Clark was pushed back to seventh place; down from sixth after the first vote.
The poll aims to whittle down the 10 candidates by giving them an idea of how much support they have from Security Council members.
Former Portuguese prime minister António Guterres remains in first place with 11 votes.
On Twitter, Miss Clark thanked those who continuted to support her and added "La lucha continua" which is Spanish for 'the fight continues'.
UN and global affairs blog editor UN dispatch Mark Leon Goldberg told Morning Report it would now be much more difficult for Miss Clark to become the next UN Secretary-General.
"She's not at the very bottom of the pack," he said.
"I would not expect her to drop out but it's certainly an uphill climb."
Mr Goldberg said Miss Clark received eight discouraged votes.
New York-based reporter Lorna Shaddick told Nine to Noon Miss Clark intends to continue in the race for the UN top job.
"She lost support between the first and the second rounds of the straw polls but she didn't lose any more, so perhaps she's interpreting that positively."
Ms Shaddick said it would have been suprising to see Helen Clark drop out of the race before the UN General Assembly, which takes place towards the end of September in New York.
Labour Party foreign affairs spokesperson David Shearer said frontrunner Mr Guterres had a great reputation, but since Russia wanted an Eastern European candidate, he may not hang on.
The rise of Slovakia's foreign minister Miroslav Lajcak to second spot showed the degree to which the votes were moving around, Mr Shearer said.
The 15-member Security Council will hold secret ballots until a consensus is reached.
For each of the candidates the voting choices are: encourage, discourage or no opinion.
In the latest poll Mr Guterres received 11 encourage, three discourage and one no opinion, diplomats said. Miss Clark received six encourage, eight discourage and one no opinion.
After second-placed Miroslav Lajcak, were Irina Bokova of Bulgaria, who is director-general of UNESCO, and former Serbian foreign minister Vuk Jeremic.
Argentinian foreign minister Susana Malcorra dropped to fifth, followed by former Macedonian foreign minister Srgjan Kerim, then Miss Clark in seventh.
Former Slovenian president Danilo Turk, Moldova's Natalia Gherman and Christiana Figueres of Costa Rica filled the last three spots.
Diplomats said the council aimed to recommend a candidate to the 193-member General Assembly for election by October. Ultimately, the five permanent veto-wielding council members - the United States, Russia, Britain, China and France - must agree on a candidate.
- RNZ / Reuters