The PSNI is set to review the case of the Hooded Men just weeks after apologising for their treatment more than 50 years ago.
The group of 14 Catholic men were subjected to what many regard as state-sanctioned torture when they were held without charge during internment in 1971.
None of the men were convicted of any offence.
In 2021, the Supreme Court ruled that the methods used "would be characterised today" as torture.
Members of the group were forced to endure what became known as the "five techniques", which included being hooded, made to stand in stress positions, subjected to loud static noise and being deprived of sleep, food and water.
In some cases the men were also thrown from helicopters they were told were at high altitude despite being just feet from the ground.
One of the group, Joe Clarke (71), who died last month, received a death bed apology from the PSNI.
Other members later received similar apologies.
Lawyers acting for some of the men have since written to British Prime Minister Rishi Sunak requesting that he now apologise for the treatment the men were forced to endure.
In 2021 a Supreme Court judge referred to a 2014 RTÉ documentary about the Hooded Men case which included a British government memorandum, known as the "Rees Memo", which "referred to the use of torture and to its approval by UK ministers".
Following the broadcast, the PSNI considered whether there was sufficient evidence to warrant a new investigation, concluding there was not.
The Supreme Court later found that the PSNI's decision was "based on a seriously flawed report, was therefore irrational, and falls to be quashed".
The PSNI has now produced terms of reference for a review that is to be carried out the Legacy Investigations Branch, which will include a trawl of records relating to the case.
An assistant chief constable, supported by legal advice, will direct any investigative action required.
If decided that the review does not provide grounds for a criminal investigation a report will be produced explaining the review process, the conclusions reached and the "rationale for those conclusions".
Hooded Men justice campaigner Jim McIlmurray said: "The surviving men and the families of the deceased are adamant they want a government apology and it would simply be the right thing to do.
"This case has been underway since June 2013 and a conclusion is required.
We lost Joe Clarke and Paddy Joe McClean and Gerry McKerr within the past decade. If the government thinks time will resolve their issue of an apology it won't as thankfully we are now seeing the children of those deceased coming forward wishing to join in our campaign for justice."
Darragh Mackin, of Phoenix Law, who represents some of the Hooded Men, said:"It is welcome news that the apology handed down by the PSNI has acted, within weeks, as a catalyst to spur a review of the torturous treatment of the Hooded Men.
"Despite this flurry of activity, the inherent lack of any response from the government remains notable.
"Today's announcement serves as a further reminder of the need for an official apology by the government and without any further delay."
A spokesman for the PSNI said that following the Supreme Court's ruling it gave an undertaking "that further materials would be reviewed and examined to ascertain if it provided credible evidence of criminal offences having been committed".
"Following consultation with Senior Counsel, terms of reference for a review have been prepared that set out a process to address the concerns raised by the UK Supreme Court," the spokesman said.
"This review will be undertaken in accordance with these terms of reference and these have been shared with the individuals, and the next of kin of deceased individuals and and/or their legal representatives.
"The Police Service will discuss and agree with the families the frequency and format of progress updates that will be provided against these terms of reference."