Nauruan president Baron Waqa claimed he brokered a deal for NZ to accept 80 refugees, which has also been denied

The New Zealand government has rejected suggestions it has blocked refugees on Nauru visiting the country on holiday visas, and that it has offered to accept 80 on a permanent basis.

The Nauruan president, Baron Waqa, said this week he had personally brokered a deal for the New Zealanders to accept 80 refugees from the island, according to a report in the Australian.

New Zealand was also among the Pacific island nations blocking holiday visas for 450 refugees, Nauruan officials told the newspaper. Despite a note from the UN supporting refugees’ travel rights, only Fiji had agreed to a request to honour the refugees’ visas, the Nauruans said.

A spokesman for the New Zealand prime minster, Jacinda Ardern, said on Friday the reported claims were “incorrect”.

He said the government had not discussed accepting a “select cohort of 80 of Nauru’s refugees” and that New Zealand “recognises valid refugee travel documents, in line with UN obligations”.

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“All applications for visitor visas for New Zealand, including from refugees, are assessed on a case-by-case basis against standard criteria,” the spokesman said.

At the Asian leaders’ meeting in Singapore this week, Ardern repeated New Zealand’s offer to Australia to resettle refugees. The Australian government is under pressure to remove the remaining children from the island – fewer than 30 now remain there.

In the interview with the Australian, Waqa also claimed 40 refugees who were sent to the United States under Australia’s deal negotiated with the Obama administration had contacted the Nauruan Departmen­t of Justice and Border Protection asking to return.

“The US – it’s a difficult place to live, a lot of competition for work and jobs,” he said. “They call America the land of the free and all that but [there are] a lot of catches and they soon find out that it’s not that easy.”

Fleur Wood, of the Aussie Diaspora Steps Up network (Ads-Up), which is in contact with about 200 refugees from Nauru to help them adapt to life in the US, said the few she knew of who had expressed interest in returning to the island were suffering from post-traumatic stress disorder or were separated from loved ones.

She said she had spoken to three asylum seekers who had expressed an interest in returning but they had not made an official request with the Nauruan authorities.

“Sometimes it’s better the devil you know,” she said.

Refugees who had been resettled in places such as Florida, Texas, Utah and New York state had faced culture shock, as well as difficulties working in low-paid jobs, but the majority were “absolutely thrilled to be in America and are making a go of it”.

“There are a few refugees who have told us that they want to go back to Nauru,” she said. “What I find is that the ones that want to go back have PTSD, health issues, they have depression, they have anxiety, or they have relationship issues, they have family on Nauru.

“We have one guy who is in love with somebody and he really wants to be in Nauru with her. Everybody’s situation is individual.”

The Nauruan government has been contacted for comment. Nauru has been criticised in the past for restrictions on media access in part due to its decision to charge journalists a non-refundable $8,000 fee to apply for a visa, with no guarantee of approval.