Dr. Frieden said Mr. Duncan’s condition and the lack of new cases were positive signs with implications for what he said will be a long fight against the disease.

“Globally, this is going to be a long hard fight,” he said. “We can never forget that the enemy here is a virus, the enemy is Ebola, not people, not countries, not communities, a virus. And it’s a virus that doesn’t spread through the air, that we do know how to control. We do know how to stop it by isolating patients, doing contact tracing and breaking the chains of transmission. I can say one week in that there are real signs of progress not only in Dallas but also around the world.”

Since Saturday, Mr. Duncan has been receiving brincidofovir — an experimental drug developed to fight smallpox and other highly infectious viruses. The C.D.C. said there are no more doses of ZMapp, another experimental drug used on two American aid workers who later recovered from Ebola.

Mr. Duncan’s nephew said that despite signs of improvement, the virus has given his uncle serious infections in his lungs and kidneys, and Mr. Duncan has not yet turned a corner toward recovery.

Mr. Duncan came to Dallas a few weeks ago from Liberia to reunite with Louise Troh, with whom he has a son. Now Ms. Troh, one of her other sons and two men who were staying with them are quarantined until late October. Local officials moved them a few days ago from a small apartment, which had towels and bedding contaminated with Ebola, to a modest four-bedroom ranch house that was donated by a church after officials were unable to find a house for the potentially infected family through traditional landlords.