It remains possible that Mikaeel Kular left his family's flat in Edinburgh of his own accord after being put to bed on Wednesday night, Police Scotland assistant chief constable Malcolm Graham said.
But he added: "It is, however, entirely possible that Mikaeel has become subject of a criminal act and our investigation has been established as a twin track to ensure that eventuality is being, and will be, fully explored."
Mr Graham gave the update at the end of a day when hundreds of volunteers helped search for any sign of the boy.
"It is of grave concern that Mikaeel has been missing for nearly 48 hours," he said.
"Since he was last seen by his mum, and all of the work we have been doing, we have been unable to confirm any sightings.
"As a result, our opera-tions and our investigations are continuing in tandem but we must make sure we examine fully every possibility as to what might have happened."
Police had already announced that officers are investigating a "potential sighting" of a child match-ing Mikaeel's description and wearing a cap.
Members of the public reported seeing a boy who was "small in build and alone" in West Pilton Gardens, Edinburgh, at around 8.30am yesterday.
However, police said Mikaeel does not usually like wearing something on his head and the child's identity could not be confirmed.
Specialist teams have been deployed from across the country to help search, investigation and comm-unity support work, Mr Graham said.
"I again make a plea if anybody out there has information which is going to assist us to better understand the circum-stances in which Mikaeel has gone missing, that they make contact with the police."
SUPERINTENDENT Liz McAinsh said there had been a "positive response" to the appeal for inform-ation in relation to the potential sighting.
She said: "We have calls that we are following up and, once we know more about that, we can report to you. You've all seen today the huge public response that we have had to this, and I would like to reiterate the thanks to everybody who has come out for our search for Mikaeel.
"That search will continue until we have any circumstances that dictate otherwise."
Ms McAinsh said other emergency services were assisting, such the fire service and Coastguard.
She said Mikaeel has not been at nursery since the Christmas break because he has been ill.
All immediate family members have been traced and spoken to by police.
"It has been extremely helpful to understand all the circumstances that have led up to his disapp-earance," Mr Graham said.
He said: "We have established a timeline of Mikaeel's movements going back for some time prior to when we can establish that he was last seen in the house on Wednesday night.
"Now it is important for us that anybody who has got information about having seen Mikaeel comes forward and gives that to us.
"There is a timeline going back of when he has been seen by different people, but I am not able to go into the detail of that at the moment."
He added: "This is an extremely significant inquiry. Everyone can get a sense of the urgency and scale of the resource that Police Scotland is putting towards estab-lishing the circumstances."
Throughout the day, volunteers stood shoulder to shoulder to scour the foreshore at nearby Cramond. Those taking part ranged from firefighters to mothers wheeling prams.
Investigations near and at the family home in Ferry Gait Crescent are continuing.
Several communal bin areas were cordoned off yesterday afternoon and four forensic officers in white suits and masks were seen entering the family home.
Officers said earlier that they had spoken to Mikaeel's father and all of the boy's relatives are said to have been very helpful to the police.
THE youngster's mother has been named locally as Rosdeep Kular, 33.
She is said to be getting support from police, her family and friends, but is "very distraught".
Scores of people gathered at the North Neighbourhood Centre in West Pilton Gardens - near the possible sighting of the youngster - to help with the search.
Neighbours, including mums with their small children in prams, joined the desperate search yesterday.
Around 400 people were seen searching fields, bushes, a nearby golf course and neighbours' homes.
Nicola Hunter, 31, from Muirhouse, who has two sons, said Mikaeel's disappearance was "every mum's worst nightmare". She said: "I just want to try and help. It's just too close to home."
Kimberly MacFadyen, 34, from Davidson's Mains, also joined the search party.
"I would be absolutely devastated if it was my wee boy. Everyone is pulling together," she said.
A telephone number set up specifically for the case has received more than 150 calls.
Calls to the 0300 200 0200 number will be answered by dedicated members of staff.
Specialist officers, police horses and sniffer dogs, and the Police Scotland helicopter have all joined the hunt.
The Child Rescue Alert system, which is usually reserved for abduction and kidnap cases, has been activated.
Police said that several people have been helping them with their inquiries but that there had been "no formal detentions".
The search for Mikaeel has concentrated in the Drylaw area where he lived, specific-ally Pennywell, Muirhouse and Silverknowes estates.
Ms McAinsh again urged local residents to check all property, including gardens, outbuildings, garages, sheds and vehicles for the youngster.
Mikaeel is described as 3ft, of Asian appearance and possibly wearing a beige hooded jacket, blue jogging bottoms, and brown Clarks shoes.
Police said the youngster has a faded scar on the bridge of his nose and a sore on the left side of his mouth.
He may also be wearing a grey pyjama top, with an embroidered turquoise dinosaur on the chest, and black gloves with multi-coloured fingers.
Anyone with any information can contact Police Scotland on 101.