Prime Minister Helen Clark confirmed court proceedings were underway against two Israelis in Auckland.
"There will be a strong and public response to this matter once the court action has concluded," she said in a statement.
Clark has not said the men are spies, but the New Zealand Herald on Saturday said authorities believed they were agents of Israel's Mossad spy agency.
Urie Zoshe Kelman, 30, and Eli Cara, 50, denied three joint charges including attempting to obtain a New Zealand passport and participating in an organised crime group to obtain a false passport.
Another man, Zev William Barkan, 37, has fled while authorities believe a fourth suspect is still in the country.
Kelman and Cara appeared briefly in Auckland District Court on Friday and were remanded on bail with strict reporting and curfew conditions before a High Court trial at a date yet to be set.
Outside court Cara denied being a Mossad member and Kelman refused to answer questions.
First known case
The case is the first known case of suspected foreign agents appearing in a New Zealand court since the 1985 arrest of two French spies who were part of a team that blew up the Greenpeace ship Rainbow Warrior in Auckland harbour, killing one man.
Documents lodged in court said police alleged Barkan tried to get a passport in the name of a New Zealander suffering from cerebral palsy.
"There will be a strong and public response to this matter once the court action has concluded"
Prime Minister, New Zealand
The passport application was sent to the Department of Internal Affairs which noted an irregularity.
Internal Affairs investigations officer Ian Tingey said he spoke to the father of the person named in the application who said his son was wheelchair bound and in institutional care. Police were tipped off and a covert operation was set up.
According to the police allegations, Barkan left the country and the passport was to be picked up by one of the other two.
A complex operation to get the passport delivered was allegedly set up by the Israelis, but it was monitored by police who picked up both Kelman and Cara.
According to the police summary, neither Cara nor Kelman had an explanation for why they were involved in wanting to obtain the New Zealand passport, nor did they say what their involvement was.
They also claimed they did not know each other.
Another police witness, Michael Zandvoort, said Kelman, whom he knew as John, told him he had a contract in Europe and would be away for two months, "something to do with West European embassies".
"John never told me specifics about the company he worked for but it was something to do with security and detecting bugs."
New Zealand passports have become increasingly sought-after on the black market, primarily because of their visa-free access to many countries including the United States.
There have been cases of Mossad agents trying to pass themselves off as nationals of neutral countries. In 1997, Mossad agents were caught using Canadian passports during a failed assassination attempt on a Muslim official in Jordan.
In 2000, a Mossad operative was handed a suspended sentence after being accused of espionage and repeated use of false identity documents in Switzerland.