Figures tendered to the PNG Supreme Court this week, and obtained by Fairfax, show that just 12.3 per cent of the detainees on Manus Island who have been processed were found not to have valid claims for protection.

This means that 87.7 per cent of people who have been assessed are refugees - an almost identical proportion to the number of boat arrivals to Australia who were later found to be genuine refugees. Figures from 2012-13 show 88 per cent of boat arrivals were found to be genuine refugees.

Despite this, many of the men on Manus Island have languished there for almost three years.

There are 1010 refugees and asylum seekers on Manus Island, the documents show, with 43 of those people remaining under the medical care of Australian authorities - a figure unchanged in two months.

The number of people processed by PNG authorities is also unchanged in the two months to June 28 - despite assurances by the PNG government that it would fast-track processing.

PNG authorities have approved 545 people for refugee status and assessed another 76 as being "non refugees".

Languishing in detention are 389 asylum seekers who are yet to have their refugee claims processed.

The Supreme Court in Waigani, PNG, is impatient with progress so far. On Wednesday it issued a two-week deadline for the remaining asylum seekers to be processed. Chief Justice Sir Salamo Injia said the process had dragged on for long enough.

The court also insisted that asylum seekers now be called "residents", after a recent Supreme Court ruling that the detention of asylum seekers at the centre was illegal.

According to a statement of claim lodged in the court, delays in processing asylum claims "and resultant uncertainties over future prospects", is one of the most frequently-made complaints by asylum seekers and refugees on Manus.

"The applicants are now beginning the third year of their accommodation at the Centre and still do not have any idea as to when they will be released."

Lawyer Ben Lomai told local media in PNG that none of the refugees and asylum seekers on Manus Island wanted to stay in PNG once their cases had been resolved.

The figures, compiled by PNG, show the highest groups of detainees on Manus Island are Iranians, Afghans, Pakistanis and stateless people.

Of the 389 still in limbo, 242 have gone through initial assessments and are waiting for the PNG Immigration Minister, Rimbink Pato, to sign off on their cases - while another 147 are yet to have their claims heard.

However, in the past two months, PNG authorities have assessed more people not to be refugees than in the past: of the 242 waiting for Mr Pato's sign-off, 127 were given negative assessments compared with positive assessments for 115 people.