The remains found in a suitcase in Ardclough, Co Kildare, have been identified as those of a male.
The body, which had been dismembered, was found in a suitcase wrapped in plastic.
A murder investigation is under way.
Gardaí believe the violent death of the man and the depositing of his remains in the canal are recent events, most likely occurring in the last four days and witness evidence is vital to the case.
Superintendent Gerry Wall said the area was popular with walkers and cyclists and appealed for anyone who was here or saw anything between last Thursday and yesterday to contact them.
The remains were found by people out walking along the Grand Canal yesterday afternoon.
Deputy State Pathologist Dr Michael Curtis carried out a preliminary examination of the scene.
The body has been removed to the morgue at Naas General Hospital.
The roadway along the canal has been sealed off as a crime scene.
The Garda Technical Bureau and the Garda Water Unit were also at the scene.