The director of the U.S. Centers for Disease Control and Prevention said Monday the agency is rethinking its approach to Ebola infection control after a Dallas nurse became infected with the disease.

The remarks underscored a shift in the outbreak response by the Obama administration. Officials initially emphasized U.S. preparedness, but have more recently acknowledged lapses in two Ebola cases at a Dallas hospital. CDC Director Tom Frieden said Monday that the U.S. needs to step up training and education to help hospitals...