Each time someone answers from an apartment inside, he begins a different routine. Sometimes he is a policeman. Other times he is Ded Moroz. Still others he is a maintenance worker or a repairman.
The point, he says, is to see if Minsk residents will open their door to someone they don't know. After all, not everyone is likely to guess that the stranger ringing their buzzer is actually a policeman -- moreover, one dressed as Grandfather Frost.
On this particular excursion, one woman was among the very few to demonstrate what he considered a healthy sense of caution.
"Open the door. No one is answering at your neighbor's flat, apartment 94," Rebkavets says into an intercom.
"If there's no one there, why should I let you in?" a woman answers.
"You're right. We're actually police officers," Rebkavets says. "We're conducting a campaign. You're doing the right thing. Never open the door to someone until you find out their name, whom they want to see, and who sent them."
It may seem strange to see a beloved holiday figure turned away from city door fronts. But police in Minsk say that is precisely the point. Crime is on the rise in the Belarusian capital, and they say residents must learn to be more wary of potential burglars and other criminals who may try to enter their homes.
Police are also looking to soften their image as iron-fisted enforcers of the autocratic regime of President Alyaksandr Lukashenka.
So law enforcement officials are hoping people will respond favorably to a visit by a new, friendlier police officer, dressed in the comforting guise of Grandfather Frost, and accompanied by a female police officer dressed as his trusty sidekick, the snow maiden Snegurochka.
Police Colonel Uladzimir Karshakou told RFE/RL's Belarus Service that officers are using the visits to inform residents about the rising number of break-ins, and to try to persuade them to install burglar alarms that would allow them to immediately contact the police in the event of a crime.
"These incidents are taking place every day," Karshakou said. "People are opening their doors to God knows who, and this often results in burglaries and other violent attacks. By installing these alarms -- something that takes just 3-5 minutes -- police can arrive at your home almost immediately if something goes wrong."
The alarms cost the equivalent of $11 per month, which may seems like an unaffordable luxury to many in Belarus, where the average monthly salary is about $225.
But even families that aren't in the market for an alarm system said they had read about the program in the newspaper and were pleased to get a personal visit from Grandfather Frost.
Officer Rebkavets was on the receiving end of a number of poems, recited in traditional fashion by the families' youngest members.
In one home, Rebkavets coaxed a poem in Belarusian, rather than Russian, out of one young boy. After some encouragement, the boy plucked up his courage and recited a poem about the legend of Belarus's Lake Narach, the country's largest lake.
But is the Grandfather Frost police action about safety and image alone? It's a pre-election season, after all -- a time when presidential hopefuls and their supporters must literally canvass door to door to collect thousands of signatures to ensure their place on the ballot.
Some are questioning whether the police are truly worried about crime -- or if they just want to ensure that fewer doors are opened when opposition candidates come knocking.
(RFE/RL's Belarus Service contributed to this report.)