Barack Obama has organised an emergency meeting on Ebola after it was confirmed that a second US nurse infected with the virus was travelling on a commercial plane the day before she fell ill.

The US president was to meet emergency officials on Thursday following the diagnosis of a nurse from Dallas who had provided care to Thomas Eric Duncan, a Liberian, who died of Ebola on October 8.

The nurse reported having a fever on Tuesday, the day after she returned home on a flight from Cleveland to Dallas, and after she had learned a colleague had contracted Ebola. 

Government officials on Wednesday said she should never have got on the plane.

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Tom Frieden, director of the Centres for Disease Control and Prevention (CDC), said no one else involved in Duncan's care will be allowed to travel "other than in a controlled environment''.

"We could've sent a more robust hospital infection control team and been more hands-on with the hospital from day one about exactly how this should be managed,'' he said Tuesday.

Infected Ebola patients are not considered contagious until they have symptoms.

Frieden said it was unlikely that other passengers or airline crew members were at risk because the nurse did not have any vomiting or bleeding.

However, the CDC has alerted the 132 passengers aboard Monday's Flight 1143 from Cleveland to Dallas' Fort Worth on Monday "because of the proximity in time between the evening flight and first report of illness the following morning''.

The woman is being treated in Texas and will be flown to a specialist hospital in Atlanta where some previous Ebola patients have recovered.