U.S. regulators are seeking a nationwide ban on menthol cigarettes, a move that would remove nearly a third of the roughly 250 billion cigarettes sold annually in the country.

The action, aimed at curbing teen use of flavored tobacco products, puts the industry into an all-too-familiar spot: defending the minty smokes popular among younger smokers and African-Americans. More than a dozen municipalities have adopted bans on menthols, but cigarette makers have so far avoided federal restrictions.

On...