A new National Unity Government formed two years ago had created new hope of a government free of corruption and self-interest, he said.
"But what do we see today?
"A President and a chief executive whose relationship is dysfunctional.
"A failure to undertake the necessary electoral reforms to enable parliamentary elections to be held, undermining the legitimacy of the current Government and sowing the seeds of future electoral disputes and instability.
"A Government that, two years into its existence, has yet to fill senior positions.
"And a host of promised reforms for improving governance and tackling corruption that are yet to be even seriously discussed, let alone implemented.
"These failings are profoundly concerning. Continued division and dysfunction within the National Unity Government threatens the progress we have made together over the past 15 years.
"So, at a time when the international community is renewing its commitment to Afghanistan, we reiterate our expectations of the Government in return."
Afghanistan's representative to the United Nations, Mahmoud Saikal, who had already spoken during the debate, chose to reply to New Zealand's statement.
He began by saying that New Zealand was a "true blue friend of Afghanistan", before shooting back at McCully's comments.
"I am sure it was in the spirit of that kind of friendship that Minister McCully had that level of frankness in his statement.
"But with all due respect, the debate over governance in Kabul is an internal matter of Afghanistan, and we expect from our friends and partners around the world to respect that and understand their limitations when it comes to the sovereignty of other countries, as we respect the sovereignty of New Zealand and all other countries around the world."
Saikal went on to defend his government's progress and leadership, and said Afghanistan's international partners should be proud of its efforts to create stability in the region.
New Zealand's representative to the UN, Gerard van Bohemen, then thanked Saikal "for the frank remark back to us".
Afghanistan is facing a new wave of violence led by the Taliban and other extremist groups.
The Special Representative of the Secretary-General in Afghanistan, Tadamichi Yamamoto, said in his statement that he was concerned increasing violence in the country was taking its toll on civilians.
"Nowhere is this trend more apparent than for children, among whom there has been an 18 per cent increase in casualties, with 388 children killed in six months," he said.
Earlier in the week, McCully also chaired a historic peace deal between the Colombian Government and the Revolutionary Armed Forces of Colombia (FARC), who have agreed to a ceasefire after more than 50 years of conflict.
