New Zealand Prime Minister John Key says the Government does not plan to get involved in resolving tension between Tonga and Fiji.
Lieutenant Colonel Ratu Tevita Uluilakeba Mara has been charged with sedition and was helped to leave Fiji by the Tongan navy last week.
Ratu Tevita is accused along with another officer, Pita Driti, of plotting last year to remove the head of Fiji's military government, Commodore Frank Bainimarama, who came to power following a coup in 2006.
An arrest warrant has been issued for Ratu Tevita in Fiji and Tonga's Prime Minister Lord Tu'ivakano on Monday indicated his country will not interfere with the court process to extradite him.
New Zealand Prime Minister John Key says it is a delicate situation.
"I don't think New Zealand should be doing anything to either heighten that tension or to escalate the issue. I think we can play our part in monitoring that and ensuring that cool heads prevail - and that's what we would hope."
Foreign Affairs Minister Murray McCully says he hopes Fiji and Tonga will show restraint. He described Colonel Mara's escape to Tonga as an unravelling of some of the relationships that have been key to Fiji's coup and its enforcement.
Mr McCully says there have been reports of growing tension between some members of the regime and the events in the last few days seem to support the reports.
"The fact that the emergency regulations in Fiji give some coercive powers to the authorities, and the fact that there are some very serious human rights breach allegations made against the regime in relation to others who have been pursued for sedition or mutiny in recent times, would have I thought diminished Colonel Mara's enthusiasm for due process in Fiji."
Mr McCully told Morning Report that the New Zealand Government had no forewarning of the latest developments and there is still speculation about what actually happened.
Tonga had said its navy had rescued Ratu Tevita in response to a distress signal.
Ratu Tevita maintains he did not flee the country, telling Radio New Zealand on Monday he was at sea fishing when he ran into difficulties and the vessel rescued him.
Commodore Bainimarama says the action by Tongan navy in entering Fiji's territorial waters to help a man charged with serious offences amounted to a breach of Fiji's sovereignty.
He urged the Tongan royal family, Prime Minister and government to stop the conspiracy by "a handful of self-interested individuals".
Power has corrupted, says army officer
In a message from Tonga, Ratu Tevita said he had witnessed from the inside how power had corrupted and how the main players had forgotten their original objectives.
He has criticised Fiji's attorney general, saying he is the real power behind a "morally and intellectually bankrupt" Commodore Bainimarama.
A former member of the regime in Fiji, Jone Baledrokadroka, says Ratu Tevita was once Commodore Bainimarama's right hand man. He says more than 50 officers have deserted the Prime Minister.
Accused of plot
Australian National University senior researcher Jon Fraenkel says the regime has said there are records of mobile phone conversations which suggest Ratu Tevita and former land forces commander Brigadier General Pita Driti were involved in some kind of plot to dislodge the commodore.
A senior lecturer at Auckland University's Centre for Pacific Studies, Steven Ratuva, says Ratu Tevita has family links with the Tongan monarchy.
Dr Ratuva doubts Tonga's prime minister knew about the navy's actions because the Tongan military is controlled by the king.
He says the government would probably have opposed giving assistance to Ratu Tevita, because of the effect it would have on diplomatic relations.