A Texas health care worker tested positive for Ebola, the first known case of the disease being contracted or transmitted in the U.S., even though she wore full protective gear while caring for a hospitalized patient who later died from the virus, health officials said Sunday.

Dr. Tom Frieden, head of the Centers for Disease Control and Prevention, said the diagnosis shows there was a breach of safety protocol, though it was not clear exactly what went wrong. All those who treated Thomas Eric Duncan are now considered potentially exposed.

The worker wore a gown, gloves, mask and shield while she cared for Duncan during his second visit to Texas Health Presbyterian Hospital, said Dr. Daniel Varga of Texas Health Resources, which runs the hospital. Frieden said the worker has not been able to identify a specific breach of protocol that might have led to her being infected.

Duncan, who arrived in the U.S. from Liberia to visit family on Sept. 20, first sought medical care for fever and abdominal pain on Sept. 25. He told a nurse he had traveled from Africa, but he was sent home. He returned Sept. 28 and was placed in isolation because of suspected Ebola. He died Wednesday.

Liberia is one of the three countries most affected by the ongoing Ebola epidemic, which has killed more than 4,000 people, almost all of them in West Africa, according to World Health Organization figures published Friday. The others are Sierra Leone and Guinea.

Texas health officials have been closely monitoring nearly 50 people who had or may have had close contact with Duncan in the days after he started showing symptoms.

The health care worker reported a fever Friday night as part of a self-monitoring regimen required by the CDC, Varga said. A preliminary state test showed the worker was positive late Saturday and the CDC confirmed the result Sunday.

Varga said another person is in isolation, and the hospital has stopped accepting new emergency room patients. Frieden said officials are now evaluating and will monitor any workers who may have been exposed while Duncan was in the hospital.

"We knew a second case could be a reality, and we've been preparing for this possibility," said Dr. David Lakey, commissioner of the Texas Department of State Health Services. "We are broadening our team in Dallas and working with extreme diligence to prevent further spread."

Dallas officials knocked on doors, made automated phone calls and passed out fliers to notify people within a four-block radius of the health care worker's apartment complex about the situation, though they said there was no reason for neighbors to be concerned.

Dallas police officers stood guard outside the complex Sunday and told people not to go inside. One said an industrial barrel outside contained hazardous waste taken from inside the building. Nearby residents periodically came out of their homes to ask about the commotion.

Kara Lutley, who lives a half-block from the complex, said she never received a call or other emergency notice and first heard about it on the news.

"I'm not overly concerned that I'll get Ebola," she said.

Officials said they also received information that there may be a pet in the health care worker's apartment, and they have a plan in place to care for the animal. They do not believe the pet has signs of having contracted Ebola.

Frieden on Sunday raised concerns about the possible breach of safety protocol and told CBS' "Face the Nation" that among the things CDC will investigate is how the workers took off protective gear, because removing it incorrectly can lead to contamination. Investigators will also look at dialysis and intubation, in which a tube is inserted into a patient's airway so a ventilator can help with breathing. Both procedures have the potential to spread infectious material.

Health care workers treating Ebola patients are among the most vulnerable, even if wearing protective gear. A Spanish nurse assistant recently became the first health care worker infected outside West Africa during the ongoing outbreak. She helped care for a missionary priest who was brought to a Madrid hospital. More than 370 health care workers in West Africa have fallen ill or died since the epidemic began earlier this year.

Ebola spreads through close contact with a symptomatic person's bodily fluids, such as blood, sweat, vomit, feces, urine, saliva or semen. Those fluids must have an entry point, like a cut or scrape or someone touching the nose, mouth or eyes with contaminated hands, or being splashed. The World Health Organization says blood, feces and vomit are the most infectious fluids, while the virus is found in saliva mostly once patients are severely ill. The whole live virus has never been culled from sweat.

Duncan, the first person in the U.S. diagnosed with Ebola, came to Dallas to visit his son, who was born in a refugee camp in Ivory Coast and brought to the U.S. as a toddler when his mother successfully applied for resettlement.

The trip was the culmination of decades of effort, friends and family members said. But when Duncan arrived in Dallas, though he showed no symptoms, he had already been exposed to Ebola. His neighbors in Liberia believe Duncan become infected when he helped a pregnant neighbor who later died from it. It was unclear if he knew about her diagnosis before traveling.