Responding to the letter from the former secretaries, the bill’s House sponsor, Henry A. Waxman, Democrat of California, said Wednesday that he believes an outright ban on menthol is not the best way to address it.

Image Newport is the largest selling menthol cigarette in America. Credit... Daniel Acker/Bloomberg News

“I’m determined to see tobacco legislation pass Congress that protects all our children,” Mr. Waxman said. “Leading public health experts have told us that giving F.D.A. the authority to ban menthol is the best way to balance both public health considerations with the reality that many adults only smoke menthol cigarettes. I’ll continue our ongoing review to make sure we are dealing with this issue in the most effective way possible."

Menthol is derived from mint and is also available synthetically. Smoking menthol-flavored cigarettes gives the mouth a cool feeling, similar to sucking on a peppermint, and can help mask the harsh taste of tobacco.

The bill’s treatment of menthol “caves to the financial interests of tobacco companies and discriminates against African-Americans  the segment of our population at greatest risk for the killing and crippling smoking-related diseases,” the letter from the former secretaries said. “It sends a message that African American youngsters are valued less than white youngsters.”

Mr. Califano said that even though the bill gives the F.D.A. the authority to remove additives it would require a lengthy process that “could go on and on and on, and you’re talking about years before you get through the administrative process and the courts.”

Mr. Califano, who served as health secretary under President Jimmy Carter, said the idea to send the letter began when Dr. Louis W. Sullivan, the health secretary during the administration of President George H. W. Bush, called him to complain about the bill’s treatment of menthol.

“We both got our blood boiling,” Mr. Califano said in a telephone interview. They also decided to contact other past health secretaries. Five of them were reached and all agreed to sign onto the letter, according to Mr. Califano, who now runs the National Center on Addiction and Substance Abuse at Columbia University.