The 11-year-old was last seen alive nine days ago shortly after his mother dropped him off just 300 yards from Meldrum Primary School in Livingston, near Edinburgh.
Amid speculation over Rory's exact time of death, detectives said they were keen to establish as much detail as possible about the boy's movements from the time he vanished, a week ago last Thursday, to the discovery of his body last Sunday afternoon.
Reports that Rory was still alive up to 48 hours after he failed to show up at school were dismissed last night by police as "unhelpful speculation" and Detective Inspector Tom Martin said: "We simply don't know at this moment in time when he died". A police spokesman said that detectives were still waiting for results of detailed forensic examinations carried out at the scene and that media speculation was both a hindrance to the investigation and upsetting for Rory's family.
On Thursday morning, officers from Lothian and Borders Police carried out a reconstruction of Rory's final journey to school, using a car similar to the one driven by his mother Michelle, 41, which dropped him at a bus stop by an underpass across from the school.
As a result of the exercise, DI Martin said police had been inundated with calls from the public offering information and that the incident-room phone lines were being manned 24 hours a day.
Following a number of calls, a spokesman for the force said they wanted to trace two men, possibly vagrants, who were seen the morning Rory disappeared on the Nellburn Path used by the boy to get to school.
The men were said to be in their 30s, 5ft 11in tall and of slim build. They were wearing denim jackets and blue jeans. One had a can of lager and the other a small bottle of beer.
He said that there were also reports of a black-clad man wearing a black deerstalker-type hat seen in the area last Wednesday and a teenager and another male sitting at a camp fire in woods on Saturday morning.
Rory's body was discovered lying beneath a ragged tent in the same woodland about 300 yards away the following afternoon.
Police believe the two people seen by the fire could be vital witnesses and have urged them to come forward.
"We are keen to trace all these people to see if they might have any further information which could be vital to our inquiry," said DI Martin.
Since the weekend, police have been sifting through details from hundreds of calls, questionnaires and statements from the public in their efforts to build up a picture of what happened to the youngster from the Adambrae area of the town.
Chief Inspector Jim Thompson said even the "minutest snippet" of information could be valuable and should be passed on to police immediately.
The hunt for the schoolboy's killer has now been stepped up, with extra officers joining the 70-strong murder squad, making it the biggest investigation in the force's history.
Yesterday, community and beat officers worked in and around schools in Livingston to provide reassurance and advice to children.Reuse content