The United States will likely see more cases of local Zika virus transmission going forward, a U.S. health official warned on Sunday, although it is unlikely to turn into a broader situation as seen in Brazil or Puerto Rico.

The comments comes after Florida authorities on Friday reported the first sign of local transmission in the continental United States, concluding that mosquitoes likely infected four people with the virus that can cause a serious birth defect.

"We definitely don't take this lightly. This is something we always anticipated and prepared for the worst," Dr. Anthony Fauci, director of the U.S. National Institute of Allergy and Infectious Diseases, said during CBS' "Face the Nation" program on Sunday. "But we do not feel this is going to turn into that broadly disseminated situation that we've seen in Brazil or that we're seeing in Puerto Rico."

He added that this is in "stark contrast" to Puerto Rico, where conditions will lead to a major outbreak.

Fauci said that health authorities are working to reduce mosquitoes in affected areas, and encouraged individuals to stay indoors, cover up and use insect repellant.

He added that "phase one" trials of one contender of the Zika vaccine will likely start in coming weeks. If that's successful, there will be wider trials beginning early 2017.