The 11-year-old's fully-clothed body was found in woods under an old tent, three days after he went missing near his school in Livingston.
At a news conference, police said his school rucksack and its contents had not been found.
Rory, from the Adambrae area of Livingston, disappeared on Thursday morning after being dropped off near Meldrum Primary School.
His body was found on Sunday about half a mile away in a wooded area. A post-mortem examination confirmed that he had been murdered.
The absence of any sightings of Rory after Thursday morning.
Detective Inspector Tom Martin told reporters at a media conference that police had not yet identified what was used to suffocate the schoolboy.
Mr Martin said Rory's mother Michelle, 41, had dropped him and his older brother off for school on Thursday.
She stopped in a bus layby in Deans East, where Rory kissed her goodbye and made his way through an underpass and into Westwood Park.
Mrs Blackhall turned her car and caught a glimpse of Rory as she drove back down the road at 0830 BST. This was the last confirmed sighting of the child.
At 1515 BST, Rory's grandfather called at the school to collect him and it was discovered then that he had not been in class all day. A major police search began after he was reported missing.
Mr Martin said: "This took place over the next three to four days and at 1pm on Sunday afternoon the fully-clothed body of Rory was found in a wooded area near to Nellburn Park, approximately three quarters of a mile north of the point that he was dropped off for school.
The underpass where Rory was last seen on Thursday
"As a result of the post-mortem examination that was carried out last night, we have now established that Rory died of asphyxiation by means of an item as yet undetermined.
"Considerable forensic examinations and tests are currently under way to try and clarify that fact for us."
Police said there were no other obvious signs of injury, although further tests were being carried out.
They are appealing for people to look for the missing navy blue Puma rucksack and its contents, which include his lunchbox and school items.
Mr Martin said officers taking part in the weekend search received reports of "a number of strangers in the vicinity of the Deans area".
"We have learned from members of the public who have stayed there for a number of years of males who have been seen in the locality in the woods and nearby paths who are clearly strangers to the area," he said.
Rory's body was covered by a worn green tent which had the words "Outbound Sierra" written in white on it.
Police said it was possible the tent had been discarded in the woods then used by Rory's killer or killers to hide his body.
Detective Superintendent Bert Swanson, who is leading the inquiry, said: "It's undoubtedly going to be a complex and a major investigation and, indeed, one of the largest the force has dealt with.
"Our thoughts are clearly now with Rory's parents who, can I say, have been extremely courageous."
The force defended the amount of time it had taken to launch a murder inquiry, stating that a post-mortem examination was necessary to establish the exact cause of death.