Between 1960 and 2005, tissue samples from 64 cases in the region were retained.

UTV's Political Editor Ken Reid said it is "quite a serious matter" and added: "There are now police liaison officers going round informing over 60 families that body parts have been retained.

"I'm also told that a number of those affected are probably quite high-profile, in the sense that they would be well-known."

UTV understands cases include IRA murder victims from north and west Belfast.

I'm told that the circumstances of these deaths range from road traffic accidents to domestic incidents to the Troubles.

UTV's Political Editor Ken Reid

In a statement, the PSNI said the Human Tissue Authority ordered an audit in 2010.

They confirmed that they had completed a full list of all Category 3 human tissue that incorporates a significant part of the body, including organs, skulls and bones.

"The audit has enabled the PSNI to identify and consider the most appropriate way of sensitively dealing with human tissue no longer required to be held for criminal investigations," the PSNI statement said.

"Specially trained Family Liaison Officers are now visiting those families affected to inform them and to discuss with them what their options now are - this is in line with the UK national guidance and in consultation with our partners.

"We know this will be an incredibly difficult time for those families involved and we will provide all the possible support we can to them."

The statement added: "The PSNI deals with families strictly on a confidential basis, therefore we cannot discuss the specific details of the samples held."

Last week, it emerged that two English police forces had retained human tissue in unexplained death cases without notifying relatives.

Under the Police and Criminal Evidence Order, the PSNI can keep material taken from bodies during post-mortems and are not obligated to get consent from relatives.

But, while they are not subject to regulation by the Human Tissue Authority, police now routinely review the reason for all continued retention of samples and endeavour to adhere to the guidance issued by the HTA.

Stormont politicians have expressed their shock over the revelation.

DUP Policing Board member Jonathan Craig said: "This news is deeply troubling.

"It is difficult to imagine any circumstance where it is acceptable to retain the body parts of a deceased person without asking permission of the family or even informing them."

Sinn Féin MLA Gerry Kelly said: "This is a shocking revelation.

"Our thoughts are with the families of those involved. It is my understanding that the process of informing the affected families has now begun."

UUP leader Mike Nesbitt said: "I am shocked because this is not just keeping them over a number of years, it's a considerable number of decades.

"How could this have been allowed to go on for so long and for what reason - those are key questions the police must answer about this."

SDLP Policing spokesperson Conall McDevitt said: "It will be a major shock for many families to find out that tissue relating to loved ones has been retained without their knowledge.

"I acknowledge that the PSNI have now put systems into place to inform families, but it is really important that past practice is fully reviewed in order to understand why proper protocols do not appear to have been in place over the period in which tissue was retained."