Police said they are “very concerned” for his welfare and urged people to check any outbuildings and sheds in case the teenager has sought shelter from the cold.
Specialist search officers from Aberdeen and Inverness have travelled to the island to help with the ongoing “extensive” searches, while support is also being provided by partner agencies.
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The 16-year-old is 6ft 2in, of slim build with short brown hair.
When last seen he was wearing a beige jumper and black jeans and may also have a red jacket and a yellow beanie hat.
Inspector David Hall said: “We are continuing to appeal for the help of the public in tracing Aleksandr, who has now been missing for over 96 hours.
“We have been reviewing CCTV and footage provided by members of the public and we now have a better idea of Aleksandr’s whereabouts prior to the sighting at the water wheel, however we still do not know where he went next.
“I urge Stornoway residents to check any outbuildings and sheds you may have in case he has sought shelter from the cold.
“I would also ask anyone with private CCTV, dashcam or doorbell footage to please review it and contact us if you think you’ve captured him passing.
“We are very concerned for this young man’s welfare. Aleksandr, if you see this, please get in touch with us and let us know you are safe.”
Anyone with information on the teenager’s whereabouts is asked to contact Police Scotland on 101 as soon as possible, quoting incident 0803 of November 18.