Refugees stranded at an Australian detention centre have plead to be sent to New Zealand instead of Australia, saying they do not want to be resettled in a country which treats them so poorly.

The group of refugees, who have been deported to Nauru by Australian authorities, said in a letter to Prime Minister Malcolm Turnbull that they did not want to live in a "cruel" country like Australia.

In a letter reported in Australian media, they said the country did not even respect the rights of its own Aboriginal people.

They said Australian workers on Nauru had treated them with cruelty and contempt, and appealed to Mr Turnbull to send them to New Zealand.

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Referring to former Australian Prime Ministers, the letter pointed to alleged human rights abuses: "Our rights have been denied by Gillard, Rudd, Abbott.

"We have suffered unimaginable cruelty and lost any hope... We do not believe you are concerned when our children are assaulted or our women raped because if you were then you would have acted."

The Nauru detention centre has been plagued by allegations of abuse by guards and poor conditions.

The refugees said: "We need a country where we can be safe and have [a] future... Please talk to the New Zealand government and allow them to take us."

Earlier this year, the Nauru refugees wrote to Prime Minister John Key to ask to be resettled in New Zealand.

Mr Key signed a deal with former Australian Prime Minister Julia Gillard in 2013 to take 150 refugees a year from Australia's offshore detention centres.

So far, Australia has not taken up that offer.

The Telegraph reported that Mr Turnbull was reluctant to send the refugees to New Zealand because it could encourage more boat people.

Mr Woodhouse said it was up to Australia to fill the 150 places and they had not done so.

"As such, the places are reallocated to the annual quota, and most recently the places were given to Syrian refugees."

The latest group of Syrian refugees, who are fleeing civil war, began arriving in New Zealand this week.