It follows the sacking and deportation of the island's sole magistrate, Peter Law, in January along with media adviser Rod Henshaw, also both Australian.



At the time, Chief Justice Geoffrey Eames issued an injunction against Nauru President Baron Waqa to prevent Law's deportation, claiming it was politically motivated to change the outcome of cases that were due to come before the courts.



The government called his comments an "attack on (Nauru's) sovereignty" and revoked his visa in retaliation.



Eames said on Thursday he had no choice but to resign, saying the ejection of Law and Henshaw were both serious breaches of the law.



"They (Nauru government) simply don't accept that as the case," he told the Australian Broadcasting Corporation.



"And as long as they don't understand that and don't accept it then the rule of law is in a very parlous state."



He added in a separate interview with the Guardian Australia: "I could not be assured that the separation of powers and the independence of the judiciary would be respected."



Eames said that the next person to take up the position of chief justice should be "extremely wary".



"I would have thought if you can effectively be dismissed because the government doesn't like your decisions, then every judge is at risk of having his independence undermined."



The Nauru government could not immediately be reached for comment.



Nauru, the world's smallest republic, covers just 21 square kilometres (8.1 square miles), and with fewer than 10,000 residents, it is the second-least populated country behind the Vatican City.



It once had one of the highest per capita incomes in the world from phosphate deposits.



However, these have now been depleted and a major source of revenue for the government comes from a deal with Australia allowing Canberra to send asylum-seekers to a detention centre on the island, which lies 42 kilometres (26 miles) south of the Equator.