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, Assistant Chief Constable Malcolm Graham, of Police Scotland, said.
"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," he said.
Mr Graham gave the update at the end of a day when hundreds of volunteers helped search the area 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 on Wednesday night by his mum, and all of the work we've been doing, we've been unable to confirm any sightings of Mikaeel.
"As a result, our operations 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 matching 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 indentity could not be confirmed.
Specialist teams have been deployed from across the country to help search, investigation and community support work, Mr Graham said.
"I again make a plea if anybody out there has information which is going to assist us in better understand the circumstances 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 information in relation to the potential sighting.
She said: "We have calls that we are following up and, once we know more about that that we can report to you, we will do that.
"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 that has come out in 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 a the fire service and Coastguard.
She said Mikaeel has not been at nursery since the Christmas break because he has been ill.