Urgent attempts are now being made to identify which soldiers the samples were drawn from.
About six body parts and more than 50 tissue samples were reportedly retained by the Royal Military Police (RMP) without relatives of the servicemen being notified.
The remains were discovered last month when a new manager was appointed at the Military Police's Special Investigations Branch (SIB).
The body parts were found at the John Radcliffe Hospital in Oxford, while the tissue samples – which were kept on laboratory slides for matching or identifying the dead soldiers – were discovered at the SIB's headquarters at Bulford Garrison in Wiltshire.
Major General James Everard, Assistant Chief of the General Staff, said the samples related to 30 service personnel dating back to 2002.
He said: "We owe a huge apology to the families involved and those who will now be feeling stressful even if it doesn't affect them."
Asked whether there could more samples still to be un-covered, Maj Gen Everard said he "hoped not".
He added: "We've checked pretty thoroughly once but I've asked for it to be done again and that process will be completed over the next few days."
Maj Gen Everard blamed a "failure of process" for the tissue samples being kept and said an investigation was under way.
He said: "There was a hint in some of the newspapers that these parts and tissue samples were being held for wider purpose. They weren't.
"These were just tissue samples that we had failed to recover post-inquest and deal with in line with the families' wishes.
"It's a failure of process, nothing more than that, but we absolutely recognise this will cause distress and we're deeply sorry."
Officials are now trying to identify and inform the families affected.
An Army spokesman said: "There are occasions when it is necessary for the RMP Special Investigations Branch to retain slides of forensic material from individuals killed on operations as part of their investigation – this is standard practice.
"However, the RMP identified there were a small number of cases where this had been done without the correct processes being followed to inform families.
"It is thought there could be 60 forensic items, such as microscope slides, which contain material from some individuals."
He added: "Investigations are being carried out urgently into this matter. The RMP Special Investigations Branch has also taken swift action to ensure this cannot happen again and are identifying the families affected as quickly as possible."
The MoD said approximately 90% of the 60 forensic items were histology slides.
It said a change in the way the SIB liaised with families was to blame for the consent not being achieved, adding that when the oversight came to light in July procedures were immediately changed.
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