And they are now watching hospital personnel as they put on and take off their protective garb, retraining the staff and evaluating the type of protective equipment being used. They were considering using cleaning products that kill the virus to spray down workers who come out of the isolation unit where the nurse is being treated.

“There are a series of things that are already implemented in the past 24 hours,” Dr. Frieden said. “If this one individual was infected, and we don’t know how within the isolation unit, then it is possible that other individuals could have been infected as well.”

The agency’s acknowledgment that substantial changes were needed came in sharp contrast to its earlier tone of confidence. On Sept. 30, Dr. Frieden had declared about Ebola: “I have no doubt that we will stop it in its tracks in the U.S.” He began Monday’s press briefing by saying that “stopping Ebola is hard.”

The additional precautions announced Monday were part of what Dr. Frieden described as a “doubling down” on the amount of training, education and support the C.D.C. provides to Texas Health Presbyterian and other hospitals around the country.