Dr. Hitchener said that the enlarged livers are not a sign of disease, and that the ducks are “physiologically normal.”

Other countries have similar bans on the sale or production, including the United Kingdom, Israel and India. Retailers such as Whole Foods banned the sale of foie gras in 1997 and Postmates stopped delivering it in 2018.

Not all foie gras comes from ducks or geese that have been force-fed; Dan Barber, a chef and a pioneer in the farm-to-table movement, gets his from ducks in Spain that naturally gorge themselves.

But for animal rights activists, New York is viewed as the most important battleground, where a tradition of foie gras consumption will go up against an increasingly progressive Council and a city “where people fight for justice,” said Matthew Dominguez, political adviser for Voters for Animal Rights.

That doesn’t mean the legislation will pass. New York City has an unsuccessful recent history of pursuing luxury-based animal rights-adjacent bans. The issue has come up three times at the state level since 2011, but did not progress far.

In one instance, Mr. de Blasio promised to ban carriage horses on his first day in office. Six years later, the carriages still operate, though they’ve been confined to Central Park. Other proposed bans on wild and exotic animals in circuses and on the sale of fur products have taken years to pass, or not passed at all.

“Historically, animal rights bills are seen as being on the back burner to a number of pressing issues affecting humans,” said Edita Birnkrant, executive director of New Yorkers for Clean, Livable, and Safe Streets, an animal rights organization.