The Centers for Disease Control and Prevention says it is monitoring 77 people who had contact with patients diagnosed with Ebola.
Seventy-six of those, CDC Director Tom Frieden said in a press conference, were health care workers who cared for Eric Duncan, the first person diagnosed with Ebola in the United States.
Frieden said Nina Pham, the nurse who contracted Ebola while caring for Duncan, had contact only with one other person before she was isolated.
Frieden says because Pham sought treatment quickly, the number of people potentially exposed to the deadly virus was limited.
David Lakey, the commissioner of the Texas Department of State Health Services, said that they have not yet identified any error in procedure that could have led to Pham's infection.
Pham, who doctors said was in stable condition, issued a statement of her own, saying she was "blessed to be cared for by the best team of doctors and nurses in the world."
"I'm doing well and want to thank everyone for their kind wishes and prayers," she said in the statement.
During the conference, Frieden said the CDC would now dispatch an "Ebola response team" that would be on the ground in hours at any hospital in the United States that has a confirmed case of Ebola.
"Caring for Ebola can be done safely but it's hard," Frieden said.
He added that looking back at Duncan's treament, he wished that the CDC had sent the kind of team they will dispatch now. He said that in the Duncan case, the CDC sent a sizable team, but they could have done more to support the hospital with infection control.
Frieden said that from now on hospitals with Ebola cases will be required to have an on-site manager who oversees infection control and the number of staff members who have contact with Ebola patients will be limited.
Frieden said that he understands that health care workers are concerned and that even "a single infection is unacceptable."