The plan, as outlined by the director of the Centers for Disease Control and Prevention and other top authorities, calls for an extra dose eight months after people get their second shot of the Pfizer or Moderna vaccine. The doses could begin the week of Sept. 20.

Health officials said people who received the single-dose Johnson & Johnson vaccine will also probably need extra shots. But they said they are awaiting more data and have yet to work out the details.

The overall plan is awaiting a Food and Drug Administration evaluation of the safety and effectiveness of a third dose, the officials said.

In a statement, health officials said it is “very clear” that the vaccines’ protection against infection wanes over time, and now, with the highly contagious delta variant spreading rapidly, “we are starting to see evidence of reduced protection against mild and moderate disease.”

“Based on our latest assessment, the current protection against severe disease, hospitalization and death could diminish in the months ahead,” they said.