Mr. Jenkins and other officials described their temporary home as a four-bedroom residence ''away from other people'' on a multi-acre property within the city limits, donated for them by an unnamed member of the Dallas faith community.
''I'm a married man with a little girl who will have her ninth birthday next week,'' Mr. Jenkins told reporters. ''I'm wearing the same shirt I was when I was in the car with that family.'' He added: ''If there were any risk, I would not expose myself or my family to that risk. But there is zero risk. These people are asymptomatic.''
On Thursday, a glitch had stopped the cleanup.
Read MoreTexas hospital record scrutinized after Ebola snafu
Kasey Bonner, the coordinator for the Cleaning Guys, the company hired to do the job, said its workers were not allowed to enter because the company did not have permission to transport hazardous material by road. ''There was no protocol put in place for handling Ebola on Texas highways,'' she said.
Mr. Jenkins said Friday evening that local officials continued to lack a state Department of Transportation permit to dispose of the materials taken from the apartment. The materials will be put in sealed plastic barrels on a trailer attached to a truck, and the truck will be stored.
''That sealed truck trailer with the sealed barrels inside of it will be guarded by deputies, until such time as the permitting can be achieved,'' he said. ''It causes no risk to the public.''
The confusion was indicative of the various local, state and federal protocols and levels of preparedness that have raised questions about the ability of the nation's health care infrastructure to handle a potential epidemic.
In Washington on Friday, while military officials announced that the Army would more than double the number of soldiers it is sending to West Africa to help contain the Ebola virus there, senior White House officials tried to play down the series of missteps in the handling of the Ebola case in Dallas. They insisted that the public health system in the United States was working effectively and would prevent an epidemic of the deadly virus from taking root in this country.
Read MoreHHS' Burwell: We have tools to stop Ebola spread
White House aides defended the administration's response, saying that the federal Centers for Disease Control and Prevention had been working closely for months with state health officials, doctors and hospitals.
Around the country, anxiety spread Friday as two hospitals in the Washington area each reported a possible case of Ebola, and a television journalist working in Liberia prepared to return to the United States after being told that he had the virus. Besides the 10 people considered most at risk in Dallas, another 40 people are being monitored in the city but are considered at relatively low risk, officials said. No one has developed any symptoms. The first signs of the illness often appear within eight to 10 days, but can take as long as 21 days.
White House officials acknowledged the public's growing nervousness, but said Americans had little to worry about.
''There's a lot of fear,'' said Dr. Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases. ''It's the unknown. It's the cataclysmic nature of it -- namely, it's acute, it kills in a high percentage.''
But he said, ''The system that's in place, with our health care infrastructure, would make it extraordinarily unlikely that we would have an outbreak.''
In a briefing with reporters on Friday, Rear Adm. John Kirby, the Pentagon press secretary, said the total United States military presence in West Africa could rise to as high as 4,000, an increase from the 3,000 that Mr. Obama announced several weeks ago. Admiral Kirby also announced that the Army itself would more than double the number of soldiers it was sending to West Africa, to 3,200.
But the White House did not announce any new initiatives in the United States to address concerns about the sometimes chaotic response in Dallas. In the last several months, officials said the C.D.C. had expanded facilities capable of testing for Ebola and had mailed detailed information six times about how to treat and contain it. On Thursday, the federal government sent another set of guidelines, they said.
But federal officials flatly rejected the idea of expanding the screening of passengers arriving from West Africa, and said they would not support calls for a ban on travel to the United States from countries being ravaged by the disease. They said such moves would be ineffective and, at worst, could prevent medical workers and other assistance from reaching Africa.
''We believe those types of steps actually impede the response,'' Lisa Monaco, the president's homeland security adviser, said of proposals to restrict air travel. ''They impede and slow down the ability of the United States and other international partners to actually get expertise and capabilities and equipment into the affected areas.''
Representative Tim Murphy, Republican of Pennsylvania, the chairman of a health oversight committee in the House, said he was ''deeply concerned'' about the travel decision, and said his committee would hold a hearing in about two weeks to examine the government's response.
Administration officials have spent the last several weeks repeatedly offering assurances that the American health system was well equipped to seamlessly handle the virus if it arrived on the country's shores. President Obama has said several times that he has confidence in the C.D.C.
But images from Monrovia, Liberia and Dallas in the last few days have raised new questions about the adequacy of the American effort on both continents.
In Liberia, the help Mr. Obama promised several weeks ago has been slow to arrive, and logistical glitches have prevented the United States military from being able to quickly set up the hospitals and treatment centers needed to halt the virus. Gen. David M. Rodriguez, commander of the Africa Command, told reporters in Washington that the military was working quickly, but that it could take ''several weeks'' to get the hospitals built and the medical personnel trained.
And in Dallas, the misstep at Texas Health Presbyterian Hospital, where Mr. Duncan is in serious condition, came after the acknowledgment Thursday by other health officials that the apartment where he had stayed had not been sanitized, with the sheets and towels that he had used while sick still there.
Dr. Ashish Jha, a professor at Harvard University's School of Public Health, said there appeared to be ''literally multiple failures'' that led to Mr. Duncan's release on Sept. 25, only to be hospitalized three days later when his symptoms worsened. Among them, he said, are that the nurse who learned Mr. Duncan had just come from Liberia failed to tell a doctor directly.
''In a well-functioning emergency department, doctors and nurses talk to each other,'' Dr. Jha said. ''Also, why didn't the physician think to ask the question separately? Anyone who comes in with a febrile illness, a travel history, that's a fundamental part of understanding what might be going on.''
He added, ''For me, the most disappointing thing isn't that the system didn't work, but in the aftermath, instead of helping every other hospital in the country understand where their system failed and learn from it, they have thrown out a whole lot of distractions.''
The criticism from the health experts contrasted sharply with the tone coming from federal officials, who said the most important thing they could do was to communicate with the public about the need to be careful and the need to remain calm.
Ms. Monaco said she was confident that the mistakes made at the hospital would not be repeated at other health facilities. She also noted that since March, when the first Ebola cases were reported in Africa, thousands of people from the affected region had flown to the United States, and there has been only one known case of Ebola.
''The United States is prepared to deal with this crisis, both at home and in the region,'' Ms. Monaco said. ''Every Ebola outbreak over the past 40 years has been stopped. We know how to do this, and we will do it again.''
—By The New York Times' Manny Fernandez in Dallas, and Michael D. Shear and Abby Goodnough from Washington. Marc Santora contributed from New York.