Helen Clark faces a crucial vote in the next 24 hours when the UN Security Council holds its third straw poll on who should be the next Secretary-General.
Helen Clark described the result of the last straw poll as disappointing. Photo: AFP
With the withdrawal of Montenegro's Foreign Minister Igor Luksic, the field has now narrowed to 10.
In the second straw poll earlier this month Ms Clark was pushed back to seventh place; down from sixth after the first vote.
Ms Clark described the result as disappointing but Prime Minister John Key and Foreign Minister Murray McCully, who have been lobbying hard for her, said she was not yet out for the count.
Each of the 15 countries can cast one of three votes: encourage, discourage or no opinion. Votes recorded for or against a candidate are made public but how each member country voted remained a secret.
John Key Photo: RNZ / Cole Eastham-Farrelly
Prime Minister John Key said so far there had been a lot of tactical voting that had benefited the Eastern European candidates.
"The question for the P5 [five permanent members] countries that aren't Russia, if you like, is to think about are they getting enough choice about the sort of candidate that they want.
"It's one thing for Russia to think it's Eastern Europe's time, but the question is what do the others think?"
He said if New Zealand could get one of those other P5 members to be a "cheerleader" for Helen Clark, that could be a game changer for her.
The five permanent members of the Security Council had the power of veto against any of the candidates.
Labour Party foreign affairs spokesperson David Shearer said the most important aspect of the polls so far was how those countries were voting.
David Shearer Photo: RNZ / Diego Opatowski
"There does seem to be a stand-off between Russia and the United States; Russia supporting an Eastern European candidate and the United States has traditionally gone against Russia and vice versa."
Mr Shearer said if that happened, that created the opportunity for Helen Clark to come through the middle.
"If there are a number of P5 members who don't want Helen Clark, that presents a bit of a problem - all votes on the Security Council are not equal."
After the result of the second poll, there was some discussion whether Helen Clark would withdraw from the race.
Green Party global affairs spokesperson Kennedy Graham said if her rankings did not improve in the poll, Ms Clark would likely review her candidacy.
"It would have to be her call, but the logic would suggest there's a limit to the number of straw polls in which you come in the middle of the pack.
"The whole point of the straw polls is that those that are not at the very top, fall away."
Dr Graham said if she was still in the middle of the pack after the third poll, he would not be surprised if she pulled out at that stage.
Labour's David Shearer said there was still a long way to go.
"We saw a big difference between the first straw poll and the second, in terms of rankings and where they moved to.
"It's not over until the fat lady sings," said Mr Shearer.
Mr Key said Helen Clark just had to take it one step at a time, as he believed she still had a chance.
"The reality is once you're out of the race, you're really out and there's no easy way to go back from that.
"So I think she's doing the right thing - yes she's having to buckle down a little if you like, and take a few risks but I do genuinely believe she's the best candidate for the job.
"I think things can change, momentum can shift."
But Mr Key said if Ms Clark could not get any movement in this next poll, she would have to reflect on whether there was anything she could do to "shift that dial".
These straw polls continue until there is a majority candidate without a single veto from a permanent member of the Council.
That name is then officially transferred to the Assembly, whose membership would then formally choose the candidate.
A decision is expected in October.