Enough of Mr. Trump’s advisers, including Ms. Conway, assured him that the move would appeal to suburban mothers who the campaign presumed had abandoned the president.

“The past administration failed to address the rising crises with opioids and fentanyl, which have claimed countless lives and devastated communities,” Ms. Conway said in a statement. “The president and the first lady refuse to look away when data show over five million youth are illegally using e-cigarettes and vaping products. The F.D.A.’s guidance balances the protection of children’s health and the protection of adults rights.”

Officials held their last meeting with the president shortly before he left for Mar-a-Lago the week before Christmas. One person briefed on what took place said he was unambiguous at the time about the ban being what he wanted to do. Still, when asked about it on New Year’s Eve, he left himself a loophole, describing it as “temporary.”

Companies had complained that a full ban on flavored e-cigarettes would put thousands of vape shops out of business, and punish adults who had switched to e-cigarettes from smoking. In recent months, Mr. Trump has publicly acknowledged the potential adverse effects on businesses and the industry, whose trade groups had lobbied White House officials regularly over the potential ban.

Administration officials have also pointed to surveys showing that teenagers prefer flavors, like mint and fruits, much more than menthol. It is unclear to what extent young vapers use open tank systems, which require that flavored liquids be added to devices that then convert them into an inhalable aerosol.

Mr. Azar said that young people “overwhelmingly prefer cartridge-based e-cigarette products,” partly because they were easy to use and, because they were smaller than open tank devices, to conceal.

Flavored pods sold by Juul, in particular, had become extremely popular among teenagers, a trend that prompted public and regulatory backlash against the San Francisco-based company. Juul has withdrawn many of its flavors from the market under public and regulatory pressure, and faces several federal and state investigations into its marketing practices.