The 25-year-old men, flanked by two representatives of Auckland's Sikh Society and the person they are staying with in Bay of Plenty, met officials for nearly two hours in Auckland yesterday.
But they have not said if they will remain in New Zealand once their visitor visas expire early next month.
Another 36 Indian "pilgrims", who failed to board their flights to Sydney to see the Pope, are still missing.
Interpreting for the men before the meeting, societyspokesman Daljit Singh said they were devastated when they discovered their visas were temporary.
"Everything was organised by the agent. This is very disappointing to them. They are feeling that they [have been] robbed."
The men were among 3000 pilgrims from 16 countries hosted by the Catholic Church in Auckland before World Youth Day events in Australia this week.
Mr Singh said the $17,000 the men's parents paid an agent to give their sons a better life was "a huge" sum. "These people are not wealthy."
"We took all the money from our parents to come to New Zealand on the basis we can establish in New Zealand," one of the men said.
The men would not reveal their faces or names because they feared for their safety once they returned to India. "They're going to disclose who were involved [in the scam]," Mr Singh said.
"These questions actually make it hard for them to return right now."
The men, from Punjab, were Catholic, unlike others among the 39 who were Hindu or Muslim.
One of them said: "We haven't breached any conditions yet. We only came in here to tell our story to immigration."
An Immigration spokesman said the men were reminded of their visa conditions.
The visas were issued in New Delhi by Immigration New Zealand officials with help from Australian immigration and information from India's Catholic Church.
New Zealand Catholic communications spokeswoman Lyndsay Freer said the church had no reason to mistrust the checks on the men.
"Everything was done in good faith."
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