Any decision about either staying on in the contest for United Nations Secretary-General, or withdrawing, is completely up to Helen Clark, Foreign Minister Murray McCully says.
He said while the results of the second ballot were disappointing, Miss Clark still had the strong backing of the government.
The former Prime Minister has reportedly been pushed back to seventh place in the latest straw poll by the council's 15 members; down from sixth after the first vote.
Mr McCully said any decision about how she proceeded was up to Miss Clark.
"We made the nomination and we'll campaign for her.
"We try and separate our role on the council from our campaign in supporting her and it'll be something she'll need to work out as the various tactical plays are made in the ballot as to which way she should go."