Its $99 test is sold only through the company’s website, and has been used by about half a million people. It analyzes the DNA in a saliva sample to tell consumers, among other things, whether they might be at a higher or lower risk of developing certain diseases.

As such DNA tests have been released in recent years, questions have been raised about whether they require F.D.A. approval and whether using them constitutes the practice of medicine, with a doctor needing to be involved. Ms. Wojcicki’s company has long held that consumers are entitled to the information in their own DNA, though it has also been talking to and meeting with the agency about how its tests could receive regulatory approval since 2009.

In its letter, the agency said, “Even after these many interactions with 23andMe, we still do not have any assurance that the firm has analytically or clinically validated the P.G.S. for its intended uses, which have expanded from the uses that the firm identified in its submissions.”

The F.D.A. also said it had not heard from the company since May. “Instead, we have become aware that you have initiated new marketing campaigns, including television commercials that, together with an increasing list of indications, show that you plan to expand the P.G.S.’s uses and consumer base without obtaining marketing authorization from F.D.A.”

The company responded Monday with a statement emphasizing its relationship with the agency.

“We recognize that we have not met the F.D.A.’s expectations regarding timeline and communication regarding our submission,” it said. “Our relationship with the F.D.A. is extremely important to us, and we are committed to fully engaging with them to address their concerns.”