A human skull and other bones were found by a person out walking at Westfields, near Shannon Bridge.
Supt Frank O’Brien said gardaí had no reason to suspect foul play but were keeping all options open in the investigation.
Deputy state pathologist Dr Michael Curtis will visit the scene this morning.
Gardaí have also called in forensic anthropologists to try and identify the remains.
Supt O’Brien said: “The remains... were exposed and not buried. We cannot say if the remains are that or a male of female at this stage. We do not know how long they have been there or what this person died from.
“While we are treating the death as suspicious, we have no indication at this point to indicate any foul play.”
It is understood some of the remains have been removed to another location to help in the forensic examination.
Supt O’Brien said that over the years gardaí had gathered and filed DNA from people whose family members have disappeared, so these can be accessed in the event of a discovery such as yesterday’s.
He said the area where the remains were discovered is not subject to flooding and was over 100 yards from the river bank and about 20m from the Condell road.
Supt O’Brien said their DNA search may have to be widened if there is no outcome from the Limerick samples.