The fact-finding mission was designed to scrutinise the Nauru detention centre to assess whether such immigration policies should be enforced in Europe as the region struggles with a migrant crisis.

But Johanne Schmidt-Nielsen of the Red-Green Alliance, whose left-wing party does not support Australia's hardline refugee stance, announced Nauru had "excluded unwanted Danish politicians", including herself, from visiting the remote island.

The decision will fuel criticism that the Nauruan government is avoiding scrutiny of alleged abuses and poor conditions experienced by asylum seekers and refugees.

"On Monday the government of the Pacific island of Nauru announced that Jacob Mark of the Socialist People's Party, Naser Khader of the Conservative People's Party and I were no longer welcome at the 48-hour visit to Nauru of the Danish Parliament's Immigration Committee," she said in a Facebook post on Tuesday.

Ms Schmidt-Nielsen said politicians from the Social Democratic Party, the far-right Danish People's Party and the governing Liberal Party were still welcome to visit Nauru. The group of six was due to depart for the island from Brisbane on Wednesday, but the trip has now been cancelled.

The MP said she and Mr Mark had publicly criticised Australia's immigration policies, however "the reason why a Danish politician with the name Naser Khader is excluded – without having criticised Nauru or Australia – is anybody's guess".

The three MPs were denied visas to Nauru.

Mr Khader, a conservative MP who was born in Syria and whose family has a Muslim background, told Fairfax Media he believed his ethnicity played a role in the decision.

"I was the first Arab and Muslim MP in Denmark ... I really don't know [why the visa was denied] but in my passport it states that I was born in Syria," he said.

"We didn't get any explanation, I can't conclude anything else except maybe it's my background.

"Two of [the other MPs] had criticised but I didn't comment on the camps, I said from the beginning I want to see them before I comment."

Mr Khader said it was unusual for a democratic country to reject a parliamentary delegation.

Ms Schmidt-Nielsen's legal and migration adviser, Niels Rohleder, told Fairfax Media that the Danish embassy in Canberra informed the delegation of the news on Monday, when the group was in Sydney.

The development comes a week after Australian Greens senator Sarah Hanson-Young declared the culture of secrecy on Nauru "out of control" after she was barred from returning to the country to investigate the plight of refugees.

Ms Schmidt-Nielsen said the Danish Ministry of Foreign Affairs had sought to intervene but "on Tuesday the Nauruan authorities announced that their decision was final".

"The Danish delegation as a whole then cancelled their visit to Nauru," she said, adding it was "deeply undemocratic" for a government to cherry-pick which foreign MPs were allowed to visit.

Ms Schmidt-Nielsen said planning for the visit had been extensive and involved authorities from Denmark, Australia and Nauru.

"It is totally unacceptable, antidemocratic and very telling of the situation on Nauru that critics are denied access. Nauru is a very closed island," she said.

While in Australia, the group met with immigration officials, toured Villawood detention centre, and met refugees and human rights advocates.

Ms Schmidt-Nielsen cited the denial of visas to journalists seen as unsympathetic to the detention centre, as well as human rights experts and other politicians.

"It is impossible to understand that Australia can defend having camps on an island where conditions are being massively criticised by the UN, Amnesty International, Save the Children, Human Rights Watch and many others and where journalists and elected officials are not welcome," she said.

Comment has been sought from the Government of Nauru.