Barack Obama has conceded it "may be appropriate" to choose an Ebola "tsar" to lead the US response against the disease.
He also said he is "not philosophically opposed" to a travel ban from the Ebola-afflicted region of West Africa "if that is the thing that is going to keep the American people safe".
But the US president said such a measure could be counter-productive.
He spoke as the first Dallas nurse to have contracted Ebola after treating an infected Liberian man was transferred to a specialist medical facility in Maryland.
Mr Obama said his team of Ebola advisers is doing "an outstanding job".
But he said several of them, including Centres for Disease Control and Prevention director Thomas Frieden and Lisa Monaco, his senior counter-terrorism adviser, are also confronting other priorities.
He noted that Mr Frieden is also dealing with flu season and Ms Monaco and national security adviser Susan Rice, with the Islamic State extremists in the Middle East.
"It may make sense for us to have one person ... so that after this initial surge of activity we can have a more regular process just to make sure we are crossing all the Ts and dotting all the Is," he said.
Calls for Mr Obama to institute a temporary travel ban grew yesterday, mainly from Republicans who said the growing outbreak in Sierra Leone, Guinea and Liberia is creating a greater travelling threat.
But Mr Obama said a ban could increase the instance of travellers avoiding detection.
"They are less likely to get screened and we may have more cases of Ebola rather than less," he said.
The president also authorised the Pentagon to call up reserve and National Guard troops if they are needed to assist in the US response to the Ebola outbreak in West Africa.
He signed an order that allows the government to call up more forces and for longer periods of time than currently authorised. There is no actual call-up at this point.
The US has committed to send up to 4,000 military personnel to West Africa to provide logistics and humanitarian assistance and help build treatment units to confront the rapidly spreading and deadly virus.
The president also placed calls to Canadian prime minister Stephen Harper and Swedish prime minister Stefan Lofven. The White House said Mr Obama and the two leaders discussed the need for an urgent international response to the epidemic in Africa.
Mr Obama cancelled a campaign trip yesterday to stay at the White House and focus on Ebola. It was the second day in a row he axed a planned trip because of the outbreak.
The National Institutes of Health said that nurse Nina Pham, 26, was being taken from Texas Health Presbyterian Hospital in Dallas to the NIH centre in Bethesda, Maryland. The NIH facility has one of four isolation units in the US.
Texas Health Presbyterian officials said on Wednesday that Ms Pham was in good condition.
As she left the Dallas hospital in an ambulance, dozens of nurses cheered and waved signs bearing messages of affection and good wishes.
She was taken to Dallas Love Field airport, where she boarded the same executive jet used to fly a co-worker to an Atlanta hospital on Wednesday.
Hospital spokesman Wendell Watson said Ms Pham's transfer is necessary because numerous employees are being monitored for symptoms and are not available to work.
She will receive care from an NIH staff that specialises in infectious disease and critical care.
A second nurse who tested positive, 29-year-old Amber Joy Vinson, has been transferred to a biohazard infectious disease centre at Emory University Hospital in Atlanta.
Ms Pham and Ms Vinson were involved in providing care to Thomas Duncan, a Liberian who died of Ebola last week at Texas Health Presbyterian.
The nurses wore protective gear including face shields, hazardous materials suits and protective footwear as they inserted catheters, drew blood and dealt with his body fluids. Still, the two somehow contracted Ebola.