"You'd have to say that Clark has had the best launch and had one of the most impressive performances before the General Assembly body," he said. "The general comment from people in New York was that she had been one of the best two."
The other was former Portuguese Prime Minister Antonio Guterres.
It is clear, however, that many countries are reserving their judgments for the time being.
Of the nine candidates in the contest, seven are from Eastern European countries. There has never been an Eastern European Secretary-General, but no clear consensus has emerged around one of them.
Argentinian foreign Minister Susana Malcorra is expected to declare before the selection process transfers to the Security Council in July.
After New York Mr McCully went on to London to meet Foreign Secretary Philip Hammond and to Germany to meet Foreign Minister Frank-Walter Steinmeier. Prime Minister John Key has been actively lobbying too and on his visit to China last week said he would be "stunned" if China vetoed Clark.
Mr McCully said there was "an acute level of sensitivity" to the interests of Eastern Europe. "For that reason countries [will not be rushing in with early commitments]."
Phase two of Helen Clark's campaign was a first round of visits to capitals of Security Council members, who will eventually recommend a candidate to the General Assembly, and other influential countries.
There is no deadline other than the appointment needing to be made before the end of the year when Ban Ki-moon's term ends.
Straw votes at the Security Council in past selections have involved member countries giving one of three ratings to candidates - encourage, discourage or no opinion - until a consensus emerges.
Debate on this article is now closed.