Gardai are investigating whether a man whose headless body was discovered in the Grand Canal was attacked at a house party.
A source also disclosed that an eastern European woman arrived at a garda station in south Dublin city on Saturday afternoon in a "highly distressed state".
It is believed this is being linked to the murder investigation.
The body, believed to be that of a man of eastern European origin, was found wrapped in plastic in a suitcase near Ardclough Bridge, Co Kildare, shortly after 3.30pm on Saturday.
The victim's head, hands and feet had been cut off in an attempt to prevent gardai from identifying the victim.
However, detectives have been able to determine that the victim was in his early 20s.
Sources have revealed that one of the lines of inquiry gardai are following is that the victim was killed on Thursday night at "a house party that got out of control".
The killer or killers then mutilated the body in a grisly attempt to prevent identification.
As dozens of gardai assisted by the Water Unit and the Garda Dog Unit continued to search for the missing head and limbs, sources said detectives were "making progress" in learning the circumstances of the man's death.
"Gardai have worked tirelessly in attempting to determine what exactly led to the grotesque manner in which the man died," they said.
"A theory that is being looked at is that the victim became involved in an altercation at a house party with a man known to him on either late Thursday night or the early hours of Friday morning.
"The situation got out of hand and the man was attacked and suffered fatal injuries.
"His body was then disposed off in the Grand Canal in what must be described as a callous manner."
Gardai have taken more than 80 witness statements from members of the public who were in the vicinity of where the body was found, and investigating officers have appealed for anyone with information to contact Leixlip Garda Station.
A post-mortem examination was carried out by Deputy State Pathologist Michael Curtis at Naas General Hospital over the weekend, but the results have so far proved inconclusive.
However, it did determine the victim did not suffer wounds to the torso.
"We're asking for the support of people who were away for the weekend, who may have returned to their premises or property and found a room disturbed or equipment moved, even an effort to clean up a room," said Supt Wall.
"An employer or employee may have seen something that doesn't fit with normal working environment."
Supt Wall also outlined the number of agencies involved in the investigation of what he called a "very horrific crime".
"The Missing Persons Investigation Bureau is involved, the National Bureau of Criminal Investigation is also involved as well as our divisional crime units," he said.
"The Garda Dog Unit is also carrying out searches along the canal, and we have had the full support of national units since early on Saturday."