But a spokesman for Helen Clark said she was "very sensitive" to Tuvalu's problems, which related to living standards and population pressures, as well as the effects of climate change.
Last year, Tuvalu's late Prime Minister Ionatana Ionatana met Helen Clark on three occasions.
It is understood places are likely to be offered to at least some Tuvaluans who want to come to New Zealand.
The island nation has a total land area of only 26 sq km, which is spread across nine coral atolls standing no more than 4.6m above sea level.
Scientists expect Tuvalu to be one of the first nations in the world to vanish as ice caps melt and waters rise.
The Tuvaluan Government is considering buying land in neighbouring nations.
But plans to buy 5670ha of land in Fiji were shelved after the coup.
About 5000 people from the island nation are already living in New Zealand.
