An Australian Senator Sarah Hanson-Young has called on the prime minister Malcolm Turnbull to intervene after Nauru refused to give her a visa.
The Senator, who has been critical of Canberra's policy to process asylum seekers in Nauru and Papua New Guinea, said the culture of secrecy on Nauru is out of control.
Fairfax Media reports that last week it was also refused a visa for Nauru without being given a reason for the rejection.
Nauru restricts media access and charges a US$6,000 non-refundable journalists visa application fee.
Last year, a reporter of The Australian was allowed into the country, but reportedly without having to pay the fee.
Australia's opposition leader Bill Shorten has again called on Mr Turnbull to accompany him on a visit to Nauru whose economy heavily relies on hosting Canberra's asylum seekers and refugees.
Conditions at the detention camps have been criticised by human rights organisations and leaked incident reports allege abuse, but both Canberra and Nauru have dismissed the findings.
Danish parliamentarians plan to visit soon amid debate in Europe about Australia's asylum seeker policies.
In April, Australia's detention camp in Papua New Guinea was declared to be illegal, with Canberra saying it will close it at a date yet to be specified.