Another two members of the protest group known as the 'Nauru 19' are seeking political asylum in Australia.
Former MP Squire Jeremiah and his cousin Rutherford Jeremiah arrived in Australia just before the Nauru Government placed a ban on members of the group travelling overseas.
The Nauru 19, who are facing charges over an anti-government protest more than four years ago, are to go to trial from Tuesday, after the Supreme Court rejected their appeal for a permanent stay to be re-imposed.
They face charges including rioting and disrupting the legislature.
Mr Jeremiah said he had no intention of returning for the trial.
"They are denying us our political rights and our constitutional rights. They are denying us our lawyers of our own choice and they are denying us a fair trial," he said.
He said Nauru's new president, Lionel Aingimea, as the secretary of justice and then the junior justice minister in the previous government, was closely involved in the pursuit of the Nauru 19.
Earlier this year, former president, Sprent Dabwido, had also sought asylum in Australia, but no decision was made before he succumbed to cancer.
'Parody of Justice'
Meanwhile, the trial is being called "a parody of justice".
The Nauru 19 is to be tried by controversial former Fiji Chief Justice Daniel Fatiaki.
That comes after dozens of legal hearings and trenchant criticism of the Nauru Government for denying the Nauru 19 their legal rights.
No legal support is being provided by the government, leaving all the defendants, who now number 15, possibly to rely on a single public defender, who was asked by Mr Fatiaki to represent all of them on Friday.
Australian lawyer, Stephen Lawrence, one of five lawyers who have previously represented the Nauru 19, said that meant those accused people would not take part in the trial.
"Because they are simply unable to and this former chief justice of Fiji looks determined to preside over what is really a parody of justice, an affront to the justice system, and an affront to the constitutional guarantees the people of Nauru are supposed to enjoy."
In 2000, Mr Fatiaki approved the abrogation of the Fiji Constitution, following the coup removing the elected prime minister Mahendra Chaudhry from office.
Working with him at that time was Michael Scott, who has also become a judge in Nauru.
Mr Fatiaki was brought in after the Nauru Government removed its previous appointment, retired Australian federal judge Geof Muecke, who had granted the Nauru 19 a permanent stay and called the government out for abuse of process.
That stay was removed earlier this year, resulting in the trial starting this week.