Calling a surge in teen use of e-cigarettes an epidemic, the head of the Food and Drug Administration said he is considering pulling all flavored e-cigarettes from the U.S. market.

After years of declining U.S. smoking rates, sales of e-cigarettes have jumped in the past year, fueled in part by online startups selling vaporizers and nicotine-laced liquids. The most popular brand, Juul, sells refills with mango, cucumber and creme flavors. Each $4 pod contains as much nicotine as a pack of cigarettes.

“The...