The Government has ruled out offering amnesties for overstayers.
The issue has arisen over an alleged scam in which Pacific Island people were sold fake visas.
Hundreds of people reportedly bought the visas during meetings in Auckland and Hamilton, many of them overstayers who were told the visas would protect them from being deported.
Police have charged the scheme's organiser Gerard Otimi with three counts of deception.
At Parliament's transport and industrial relations select committee hearing today, Green MP Keith Locke asked Immigration Minister Jonathan Coleman about the case, saying it showed the lengths overstayers would go to.
"Have you given consideration to an amnesty for settled overstayers who have contributed to society and haven't committed any crime?"
Dr Coleman said the Government had looked at the issue but decided amnesties did not work.
In 2000, when there were 20,700 overstayers, only 5000 took the opportunity, he said.
"But 18 months later the numbers of overstayers in total had actually exceeded the numbers pre-amnesty. So amnesties don't seem to work in terms of decreasing the overall numbers of overstayers."
Dr Coleman said the Government did not want people to think of overstaying as an avenue towards residency.
"Overstaying is not a pathway to staying in New Zealand. We certainly don't want to send that message through by offering an amnesty.
"The message really is, if people are concerned about their legal status they should come forward and work with Immigration New Zealand."
He said if people came forward voluntarily their chances of staying were far higher than if apprehended by authorities.
New Zealand has about 16,000 overstayers, of which a third are from Samoa and Tonga.
Dr Coleman said there was a Pacific access category.
"We are not considering extending pathways to migration at this stage."
