The W.H.O. published its own revised estimates of the outbreak on Monday, predicting more than 20,000 cases by Nov. 2 if control does not improve. That figure is more conservative than the one from the C.D.C., but the W.H.O. report also noted that many cases were unreported and said that without effective help, the three most affected countries would soon be reporting thousands of cases and deaths per week. It said its projections were similar to those from the C.D.C.

The W.H.O. report also raised, for the first time, the possibility that the disease would not be stopped but could become endemic in West Africa, meaning that it could become a constant presence there.

President Obama’s promise last week to send 3,000 military personnel to Liberia and to build 17 hospitals there, each with 100 beds, was part of the solution, Dr. Frieden said. But it was not clear when those hospitals would be ready, or who would staff them.

Dr. Frieden said the Defense Department had already delivered parts of a 25-bed unit that would soon be set up to treat health workers who become infected, a safety measure he said was important to help encourage health professionals to volunteer. He said that more aid groups were also arriving in the region to set up treatment centers, and that a “surge” of help would “break the back of the epidemic.”

Dr. Jack Chow, a professor of global health at Carnegie Mellon University and a former W.H.O. official, said, “The surge only becomes realized when those beds are up and operating and the workers are delivering care.”

He added, “If even the medium case comes to pass, with, say, 700,000 cases by January, the epidemic will quickly overwhelm the capabilities that the U.S. plans to send.”