The vast majority of Zika cases have been and will continue to be in people who have traveled to the other countries where the virus has spread widely, or have had sexual relations with someone who traveled to those places, officials said. There have been 2,260 cases of Zika reported in the continental United States and Hawaii, including 529 in pregnant women, the C.D.C. said Friday.

So far, 36 cases of locally transmitted Zika have been identified, all in Florida, and 25 of them are linked to an area around two small businesses in Wynwood, north of downtown Miami. On Aug. 1, the C.D.C. advised pregnant women not to travel to a one-square-mile area in Wynwood. And while Gov. Rick Scott and the Florida Health Department have announced that 17 blocks of that area have been found to be clear of Zika transmission, the C.D.C. maintains that the one-square-mile section should still be considered an active Zika zone, Dr. Petersen said.

Mr. Scott also struck a different note from the federal health officials about the risks of Zika posed to Miami-Dade County, a sprawling multicultural metropolis of 2.7 million people. He minimized the extent of the spread, saying in a news conference, “We have two small areas. One less than a mile, and we’ve already been able to reduce the footprint. We have another area now that’s 1.5 miles on Miami Beach. That’s out of a state that takes 15 hours to drive from Key West to Pensacola, so let’s put things in perspective.”

His communications director, Jackie Schutz, said Friday that Mr. Scott “is encouraging people to come to Miami, to come to South Beach. Just remove standing water and wear bug spray.”

But Dr. Frieden noted that there have been several other cases of suspected local transmission in Miami-Dade County that are believed to be isolated cases. Other cases will likely crop up, he said.