One-month entry visas have now expired for a group of Indian pilgrims who disappeared in New Zealand while on a stopover en route to World Youth Day in Sydney.

A Department of Labour spokesman said on Monday that of the 40 pilgrims who arrived last month, four had returned home and 36 remained in the country, all except one on an expired visa.

Authorities knew the whereabouts of 20, including one man who approached officials last week saying he also wanted to return home.

The spokesman said 11 had come forward to seek permission to stay - eight applying for student permits and three for visitor permits.

"We are looking for the other 16," he said.

"We'll be working with the Indian community and our own networks, as we have been doing for the last few weeks, to locate them."

The spokesman said a 42-day grace period had begun, during which the pilgrims could apply to stay.

They were unlawfully in New Zealand but could not be forcibly removed during this time, he said.

The fate of those who have applied to stay should be known within the 42 days, the spokesman said.

"We are giving them some priority."

Immigration officials have warned the missing Indians that if they had to be removed from New Zealand they would be banned from any form of re-entry for five years.

Members of the group were believed to have paid $NZ17,000 ($A13,500) to an agent in India who organised their travel visas and told them they could stay in New Zealand "forever".

The department spokesman said that officials were continuing to gather information about alleged fraud and would eventually decide whether to pass it on to Indian authorities.