The chief spokesman for Health Secretary Robert F. Kennedy Jr. resigned on Wednesday in protest over the administration’s push to allow major tobacco companies to begin selling flavored vapes that appeal to children. His departure came one day after the head of the Food and Drug Administration quit for the same reason.

In a letter to Mr. Trump, obtained by The New York Times, the spokesman, Rich Danker, did not blame the president, whom he said had “twice restored our prosperity and national security against all odds.” But he warned that authorizing flavored e-cigarettes would draw more children into vaping and increase their risk for a number of health issues, from addiction to cancer.

The letter cited unnamed “senior H.H.S. officials,” other than Mr. Kennedy, who were behind steps including a new policy posted on the F.D.A. website on Friday, in which the agency said it would take steps to remove illicit e-cigarettes from the market and allow sales of those that have already crossed hurdles toward agency approval.

Dr. Marty Makary, the F.D.A. commissioner, who resigned on Tuesday, sought to block the marketing of flavored e-cigarettes, but was overruled. Mr. Trump was personally involved advancing it. In his letter, Mr. Danker did not name Dr. Makary, but he echoed Dr. Makary’s objections.

“Senior H.H.S. officials in the immediate office of the secretary have in recent months sought U.S. Food and Drug Administration marketing approval of e-cigarette flavors that would appeal to children and expose them to nicotine addiction, lung damage and higher risk of cancer,” Mr. Danker wrote.

Mr. Danker added that routine approval of the products would undermine a policy the agency issued in March, “with the support of the White House.”

Mr. Danker’s resignation comes at a particularly fraught time for the Department of Health and Human Services. With Dr. Makary’s resignation on Tuesday, the department now has three major vacancies. The positions of surgeon general and director of the Centers for Disease Control and Prevention are also unfilled.

As the assistant secretary for public affairs for the Department of Health and Human Services, Mr. Danker was responsible for coordinating the department’s outward communications. He was in Los Angeles on Wednesday, where Mr. Kennedy is speaking at a conference on the possible link between diet and cancer.

He is the second assistant secretary for public affairs to quit. Thomas Corry, Mr. Kennedy’s first top spokesman, resigned after two weeks, partly in protest of the way Mr. Kennedy handled a measles outbreak in Texas.