Texas health officials are monitoring 50 people for Ebola exposure, 10 of them at high risk of the disease after close contact with the first diagnosed US patient.
Meanwhile, leading US health authorities sought to reassure the public that an outbreak of Ebola in the United States was unlikely due to the nation's modern healthcare system.
The 50 were narrowed down from an initial pool of 100 people thought to have come into contact with the sick man.
For the next three weeks they will be checked for fever twice daily, and are currently "doing well," said David Lakey, commissioner of the Texas Department of State Health Services.
"Most of these individuals are low risk. There are about 10 individuals that are at high risk, so we are watching those individuals very carefully."
The people are health care workers and those who came in close contact with Thomas Eric Duncan, who travelled from Liberia to Texas in late September and was announced Tuesday as the first diagnosed US case of Ebola.
Anthony Fauci, the head of the National Institute for Allergy and Infectious Diseases, told a White House news conference that the US health care system "would make it extraordinarily unlikely that we would have an outbreak."
He acknowledged "missteps" in the way Dallas handled the situation at first, with the hospital admitting a flaw in electronic health records left doctors unaware of the patient's travel history to Africa.
Duncan was sent home after initially seeking treatment, and was in the community, showing symptoms and therefore contagious, for four days before he was isolated.
"There were things that did not go the way they should have in Dallas, but there were a lot of things that went right and are going right," Fauci said.
"Contract tracing is now going on, and that is the important thing."
Duncan's girlfriend and three members of her family have been ordered to stay inside in a Dallas apartment under police guard.
A hazardous materials team arrived Friday to remove the sheets and towels Duncan used while he was sick, according to pictures posted online by the Dallas City Hall.
A clean-up team was turned away on Thursday over problems with permits for dangerous waste.
Centers for Disease Control and Prevention officials continue to monitor the health of the four people in the apartment, but Duncan's girlfriend, Louise, has complained of the quarantine.
The family has been ordered to stay in the apartment until October 19, the end of the virus's incubation period.
Meanwhile, concerns mounted elsewhere in the United States about the potential spread of Ebola, which has already killed 3,338 people in West Africa.
A patient with Ebola-like symptoms - which can include fever, vomiting and diarrhoea - who recently travelled to Nigeria was hospitalised at Howard University in Washington.
A 33-year-old American cameraman for NBC News was diagnosed with Ebola in Liberia on Thursday and was said to be returning to the United States for treatment.
