The impact of the deal on Iran's economy would be "huge", Mr McCully said.
Trade delegations were already visiting Iran in anticipation of sanctions lifting, and New Zealand's trade with Iran would likely benefit if the deal was successful.
The UN meeting was at times stormy, with the US and Iran trading verbal blows in the council chamber.
Within minutes the resolution was condemned by the Israel's UN Ambassador Ron Prosor, who said the council had awarded a great prize to the most dangerous country in the world.
Mr McCully said "a number of steps remain" before the agreement can be fully implemented, including EU and US Congressional approval, and International Atomic Energy Agency (IAEA) verification.
"We urge all parties, and in particular Iran, to approach implementation with the same positive intent and good faith that led to the agreement being concluded."
If that happened and Iran stuck to its obligations, Mr McCully said the deal could help reset relations between Iran and its neighbours, including Israel.