Hong Kong's government says the widely criticised law is required to bring order to a city that saw mass pro-democracy protests previous year which often turned violent.
New Zealand is the final member of the "Five Eyes" intelligence-sharing alliance to take such action after the U.S., Australia, Canada and Britain previously announced similar measures.
Mr Wang accused the countries of having used the national security law as "an excuse to unilaterally announce the suspension of extradition treaties" with Hong Kong.
The Trump administration said Hong Kong would no longer be treated as an autonomous trading area.
Australia-China relations have become increasingly frosty over the past year, with China advising tourists and worldwide students not to travel to Australia due to "racist incidents against Asians".
Hawaii prepares for hurricane; Countries tighten COVID-19 restrictions
Hawaiian Airlines canceled all Sunday flights in between Hawaii and the USA mainland and likewise in between the other islands. Every day since Thursday, Hawaii has reported record highs of newly confirmed cases, including 73 on Saturday.
Recorded Future also asserted that one of the hacking attacks included a fake letter delivered to the current head of the Hong Kong Study Mission to China in connection with the death of a Chinese Catholic bishop.
"In light of this, it is important that New Zealand responds proportionately and deliberately to the passage of the national security law".
The law punishes crimes of secession, subversion, terrorism and collusion with foreign forces with up to life in prison.
Longer term, questions are being raised about Hong Kong's role as a leading global finance centre, after Beijing imposed a sweeping new security law on the city on July 1, heralding a more authoritarian era for China's freest city.
The report said that if the United States were to take the extreme action of cutting off some Chinese banks' access to dollar settlements, China should also consider stopping using the USA dollar as the anchor currency for its foreign exchange controls.
Under the 50-year agreement, China enshrined civil liberties - including the right to protest, freedom of speech and the independence of the judiciary - in Hong Kong's Basic Law, an approach which came to be known as "one country, two systems".
The advance readings showed consumption and investment remained weak in the second quarter, though activity likely drew some support from a strong bounce in China's economy and from the Hong Kong government's stimulus measures.