The Labour Party is calling on the Government to get involved in the overstayer problem and liaise with community leaders to look for solutions.
The overstayer issue has been highlighted by an alleged scam in which Pacific Island people were sold fake visas.
Police have charged the scheme's organiser, Gerard Otimi, with three counts of deception.
New Zealand has about 16,000 overstayers, of which a third are from Samoa and Tonga.
Labour's Pacific Island affairs spokeswoman, Luamanuvao Winnie Laban, said today it was time for the Government to do something about it.
"The recent visa scam highlighted the desperation of many in the Pacific community, as have recent submissions to Parliament's foreign affairs and defence select committee which is inquiring into New Zealand's relationship with the Pacific," she said.
"The committee has been told hundreds of children are not attending school because their parents are in the country illegally and that many are also not seeking the health care they need."
Ms Laban said Pacific Island Affairs Minister Georgina te Heuheu, and her ministry, should begin organising meetings with the Pacific community and church leaders to discuss ways to tackle the problem.
"The minister's silence has been deafening and it's time she stepped up," Ms Laban said.
Immigration Minister Jonathan Coleman was questioned about overstayers during a select committee hearing last week.
He said the Government was not considering an amnesty for overstayers because amnesties did not work in the long term.
Dr Coleman said there was an amnesty in 2000, when there were 20,700 overstayers, and only 5000 took the opportunity.
"But 18 months later the numbers of overstayers in total had actually exceeded the numbers pre-amnesty," he told the committee.