The Australian government has rejected calls to expedite visa applications of 30,000 asylum seekers who have been stuck in legal limbo in the country for more than five years, a report shows.

The plight of hundreds of refugees held in Australia’s offshore detention centres on Nauru and Papua New Guinea’s Manus Island has long been in the global spotlight.

But rights groups and the opposition have called on the government to address challenges faced by those in Australia.

In a report released on Wednesday, the Australian Human Rights Commission detailed 31 recommendations it said would improve protections for 30,000 refugees who arrived in Australia before the start of 2014, including fast-tracking their visa applications.

Canberra has rejected all of the recommendations, the report shows.

Known as the “legacy caseload”, the refugees were part of an unprecedented wave of asylum seekers who attempted to reach Australia by boat between 2009 and 2013.

Most of them are able to live among the general population – and some are able to work, depending on their status.

But the wave of arrivals saw the government institute its controversial offshore processing policy that saw new boat arrivals sent to Nauru and Manus.

The Commission said policy changes over time mean the onshore refugees have still not had their claims assessed, so they remain ineligible for permanent residency status and have limited access to support services.

“These people face prolonged delays in assessing their refugee claims, with limited government support to meet their health and other needs,” Human Rights Commissioner Edward Santow said in a statement.

“They risk severe deterioration in their living conditions and mental health, with many at higher risk of suicide.”

The Home Affairs Department said in its response that many of the group do have to access the same financial, education and health services available to other Australians.

The Opposition Labour Party has also called on the government to act.

“The government needs to come forward and explain how this is going to work with these people within our society,” deputy party leader Richard Marles told the ABC.

“It is absolutely critical that we do not develop a significant underclass in Australia and that is why the government needs to explain what its plans are for this group.”