Australian journalists reporting on the plight of asylum seekers at Nauru have been left "humiliated" by a recent election that returned the island's administration, a senior government minister claims.

In an offbeat statement released on Thursday morning, Nauru Justice Minister David Adeang said the election results on the island, which hosts a controversial Australian-funded detention centre, showed that Australian and New Zealand media should "show more respect" to Nauru's government and people.

The government of president Baron Waqa was returned with an increased majority.

Mr Adeang's statements follow long-held international concerns over governance at the Pacific island nation. Foreign Minister Julie Bishop last year sought assurances that the rule of law was being upheld at Nauru, after several opposition MPs were arrested and others had their passports seized.