The Immigration Service hopes to track down and speak with the rest of a group of missing Indians within the next few days.
Three of the 39 who disappeared en route to World Youth Day in Australia spoke with officials in Auckland on Thursday about their involvement in a visa scam.
It is understood some of them paid up to $NZ17,000 to a middle man in India.
The men say they have not tried to cheat the immigration system. They say they are victims, having paid a lifetime's worth of wages for visas they thought would help them start a new life in New Zealand.
The men say they borrowed from money lenders to pay for the visas and fear for the safety of their families and themselves if they are forced to return to India.
Immigration officials say they are continuing to work with the Indian community to find and talk with the other 36 runaways.