Their comments came as it was announced UK Foreign Secretary Boris Johnson will take part in emergency talks with his Iranian counterpart in Brussels next week.
European diplomats complained that the approach was too rigid and would rewrite the 2015 Iran agreement they had signed.
Oil tanker owners are facing a nervous wait to find out whether they can carry on doing business with Iran after President Trump said on Tuesday he was reinstating a raft of sanctions against the Persian Gulf country.
"If the government of New Zealand obeys any sanction against Iran, it is not sanction against Iran it is a sanction against the New Zealand companies", Mr Mianji said.
Foreign companies that do business in the country have also been banned from accessing American banking and financial systems.
Oil market watchers also expect that American producers will also respond to higher prices by drilling more.
In the past, sanctions against Iran have cut the country's crude exports by around 1 million barrels a day.
"In the short to medium term, I do not envisage a fall in Iranian exports to below one million barrels a day". Today, White House National Security Adviser John Bolton said sanctions on European firms were "possible".
He told CNN's State of the Union: "The Europeans will see that it's in their interests to come along with us".
The envoy added that the British government's position is clear regarding the necessity to stop Iranian interferences in the internal affairs of the region's countries, such as Syria and Yemen.
"However, if they resist the pressure from America, then I expect to see a small number of refineries being targeted by the USA treasury - imposing heavy fines on them to make an example for other refineries".
"If the nuclear deal is to continue, the interests of the people of Iran must be assured", Zarif added.
Where does New Zealand stand?
Germany and France have significant trade links with Iran and remain committed to the nuclear agreement, as does Britain, and the three countries' foreign ministers plan to meet on Tuesday to discuss it.
Emadi further said "the significance of this group is that without their payments in hard currency, the Iranian economy will face a currency crisis created by the shortfall of its earning of dollar and euro".
"I heard one of the primary industry representatives postulating that it might mean, if nothing else, that it's more hard to increase exports to iran who, of course, used to be a much larger trading partner of New Zealand than they are even now", Mr Parker said.
He said Iran would attempt to save the nuclear deal through negotiations with the European nations who were co-signatories to the deal.
As those sanctions kick in, it will have an even broader effect as well, Bolton said. The expectation that sanctions will again frustrate Iran's oil industry and limit global supply has helped to boost prices close to 5% since the announcement.
Germany said it would spend the next few months trying to persuade Washington to change its mind.
Germany's minister for economic affairs, Peter Altmaier, said on Sunday that Berlin would try to "persuade the USA government to change its behavior".