More than 100 New Zealanders and Australians of Cook Islands descent are stranded on Pukapuka in the northern Cook Islands.
They went there before Christmas to celebrate the 150th anniversary of the arrival of Christianity on the island.
The visitors were to have sailed to Samoa to catchflights home after the holidays, but they have been unable to secure a vessel, Radio New Zealand International reports.
Pukapuka - also known as Danger Island - is the most isolated atoll in the Cooks group.
It comprises three islets and a sandbank 1150km northwest of Rarotonga.
Air Rarotonga does not fly there regularly.
The Department of Port Administration in American Samoa said last week that it was awaiting approval from the US Coast Guard for a local vessel, the MV Sili, to sail to Pukapuka.
The port director, Matagi Ray McMoore, said the New Zealanders and many of the other people stuck on the island had asked to be ferried to Samoa so they could catch flights home.
But the MV Sili does not have a certificate to operate international voyages and the US Coast Guard would have to approve the special sailing.
Mr McMoore said he had been told by the office of Eni Faleomavaega, the Democrat congressman for American Samoa, that picking up the stranded travellers from Pukapuka was not an emergency and a request to the Coast Guard was not warranted.
About 180 people with links to Pukapuka stopped off in Samoa last month before travelling to the island.
A spokesman for the visitors told a Samoan television station before their trip to the atoll that the people of Pukapuka believed they originated from Samoa, with the last links going back to the 1950s when a merchant ship from Apia used to make regular voyages between the two islands.
The Pukapukan community group based in New Zealand was led by Nuku Rapana who told Radio New Zealand International his people shared links with Samoa.
"Our language itself is a unique language ... in the Cook Islands group," he said.
In 2005 Pukapuka was hit by five cyclones, which demolished 75 per cent of the houses on the island.
