More than two dozen state attorneys general urged the Food and Drug Administration on Friday to impose restrictions on electronic cigarettes, including prohibiting television advertising and banning the wide variety of candy and fruit flavors that have helped make e-cigarettes popular.

Such curbs would be far tougher than those proposed in April by the FDA. At the time, the agency said it planned to prohibit the sale of the battery-powered devices to anyone under age 18 but stopped short of proposing restrictions on advertising,...