Mikaeel Kular's mother found his bed empty yesterday morning at the family home in Edinburgh.
Police said last night that several people were 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, specifically the Pennywell, Muirhouse and Silverknowes estates.
Police brought in sniffer dogs and helicopters, and were aided by coastguard and lifeboat teams as the search extended to the coastline.
The toddler was last seen at his family's flat in Ferry Gait Crescent.
His jacket and shoes are missing and police are looking into whether he might have left of his own accord.
Police said there is currently no evidence of criminal behaviour.
A dedicated telephone number has been set up for anyone who has seen the child or has information about his whereabouts.
Neighbours on the housing estate have joined the search for Mikaeel, a twin with three other siblings.
One resident, who did not want to give her name, said: "I got woken up at the back of 7am by the police, asking if I'd seen the wee one.
"I've got a child. It's just absolutely horrific.
"I didn't see anything out of the ordinary. The first thing I did was actually search the stair."
The neighbour said a group of about 10 mothers have been out in their cars searching the area.
Police Scotland Superintendent Liz McAinsh said the force is using all the resources at its disposal in the hunt.
Asked whether there were any child custody issues with the family, she said: "Obviously we are following all lines of inquiry, there are no concerns that we have at the moment.
"We are following all lines of inquiry with all partner agencies and with the family and the family are being very helpful at the moment.
"As you can imagine, Mikaeel's mother is distraught. She just wants our help and the public's help in finding her boy."
The search is focusing on the Pennywell and Muirhouse areas. Coastguard and lifeboat teams have meanwhile been scouring the shoreline in the Cramond and Drylaw areas.
Mikaeel is described as 3ft tall, of Asian appearance and possibly wearing a beige hooded jacket, blue jogging bottoms, brown Clarks shoes and nightwear.
The youngster attends a local nursery and Ms McAinsh said: "They say Mikaeel is a friendly, playful wee boy and they are obviously concerned for his safety."
The dedicated number for anyone with information on the child's disappearance is 0300 200 0200.
The telephone line has been established as part of a Child Rescue Alert, supported by all police forces across the UK.
Local residents are being asked to urgently check all property, including gardens, outbuildings, garages, sheds and vehicles for the youngster.
Temperatures in Edinburgh dropped to 2.3C (36F) last night.
Robert Pearson, chairman of a local residents' group, said he sent out a plea for help earlier and around 50 people responded.
He said: "We split up into groups of seven to search the area. My group are currently going through the Silverknowes Golf Course but we are fearful that we might not have much hours left of light as it begins to get darker.
"We are liaising with Police Scotland and will continue to do so until they say it is unsafe to carry on searching. At the moment they have roughly 70 officers searching the area, but the mood amongst the volunteers is that it is feeling quite desperate just now."
Neighbour Linda Slattie, 52, said: "We were out this morning looking, down to Muirhouse Park, the community centre, looking in bushes and lock ups and things like that.
"I've been very shocked. It could be any one of our kids."
Police later released a more detailed description of Mikaeel, adding that the youngster has a faded scar on the bridge of his nose and a sore on the left hand side of his mouth.
He may be wearing a grey pyjama top with an embroidered turquoise dinosaur on the chest and black gloves with multi-coloured fingers.
Ms McAinsh added: "There have been no arrests. There have been no formal detentions, but several people are assisting us with our inquiries"