Mayor Bill de Blasio prides himself on confronting New York’s knottiest civic problems, such as expanding classroom time for preschoolers and lowering the cost of urban housing.

Now his administration is sinking its teeth into a friskier challenge: legalizing ferrets.

The city’s Department of Health and Mental Hygiene is urging the repeal of a policy that prohibits New Yorkers from keeping ferrets as pets, declaring that the musky, sharp-toothed mammals pose no greater risk to the public than other domesticated creatures.

The turnaround on ferrets, confirmed by city officials on Tuesday, would bolster the image of a mammal-friendly mayor who has pledged to turn New York into a kinder place for its four-legged residents, notably the horses that work in Central Park.

And it would be the de Blasio administration’s latest effort to roll back the more controversial policies of former Mayor Rudolph W. Giuliani, who instituted the ferret ban in 1999 and once accused an advocate for the animals of suffering from “a sickness.”