Dense tissue makes cancer harder to find on mammograms because the tissue and tumors both show up as white and blend together. Fat looks black, so tumors stand out more in fatty breasts.

About three dozen states already require that women be given information about breast density. The new F.D.A. rules propose specific language that would be used nationwide to explain breast density, note that some women may need more imaging tests and recommend that patients talk to their doctors about their results.

The F.D.A. language would be the minimum required, but states would be free to require more information, Dr. Jeff Shuren, director of the agency’s Center for Devices and Radiological Health, said in a news briefing.

Some in the medical profession have objected to this type of notification, arguing that not all women with dense tissue have the same increased risk of breast cancer, and that reporting the condition could frighten women and lead to a flood of unnecessary screening tests and biopsies. Doctors have also said that many of the state-mandated letters were too hard for patients to understand.

The F.D.A. commissioner, Dr. Scott Gottlieb, who will be leaving the agency on April 5, said in an interview that the new proposal had been high on the list of actions he hoped to take before departing. He acknowledged that some physicians opposed notifying women about breast density, but he said women had a right to receive the information and decide what to do about it.