They include no tax exemption of foreign income, automatic exchange of information with foreigh tax authorities in the jurisdictions where the settlers and beneficiaries are resident, and a public register of trust ownership and details.
Acting Prime Minister Gerry Brownlee had not yet responded to the story when Newshub went to air.
The union is New Zealand's largest trading partner, with about $20 billion worth of exports a year. Negotiations have also begun on a free trade deal with the union, Newshub reported.
European Commissioner for Economic and Financial Affairs Pierre Moscovici said there would be no exceptions to the crack-down.
"Let's call a spade a spade. Non-cooperative jurisdictions are tax havens. We have to list them through a common EU blacklist and to be ready hit them with appropriate sanctions if they refuse to change.
"When a country is on that sort of list, it already knows that the eyes are on it or her and that media are there, that investigations start and the first motivation of the country is to get out of it."
MPs from the European Parliament also cherry-picked New Zealand's tax laws as problematic, with Michael Theurer saying it wasn't on the radar until the Panama Papers were leaked, Newshub reported.
"New Zealand was not so much under scrutiny. But with the revelation of the Panama Papers, some newspapers and electronic media reported that there are thousands of letterbox companies, and we have to investigate that.
"I really believe New Zealand will cooperate because it's a common interest now in the OECD to find a global standard which will stop the most harmful tax practices and create a fair platform for tax competition."
Revenue Minister Michael Woodhouse said he was aware from its website that the European Parliament had set up a committee to look into the matters raised in relation to the Panama Papers.
It was set up in June, and planned to report in twelve months.
"We have not received any advice from the European Commission that action is being considered against New Zealand.
"The Government is confident that any objective inquiry will come to the same conclusion that the OECD and the Global forum on Transparency and Exchange of Information for Tax Purposes did when they reviewed New Zealand's tax settings and found us to be fully compliant with OECD standards."
"While our tax settings are sound by international standards, the Government was always open to making improvements to New Zealand's already strong tax settings if that was warranted."
That was why the Government had agreed to act on all of the recommendations from the Shewan Inquiry to ensure New Zealand's disclosure rules were fit for purpose.
"It is worth noting that foreign trust rules are just one part of a significant work programme to strengthen New Zealand's tax laws and keep them in line with international best practice.
"We have been working intensively with the OECD to develop a global response to Base erosion and profit shifting tax strategies."
