According to the World Health Organization (WHO), a major outbreak of Ebola in the US and elsewhere in the West is unlikely given the strong health systems.
President Barack Obama also said the risk of Americans getting the virus was “extremely low”, although he ordered a “much more aggressive response”.
Meanwhile authorities are investigating how Nurse Amber Vinson, who was infected when treating Thomas Eric Duncan in Texas, was allowed to travel on a plane.
Officials are trying to trace the 132 people who flew with Amber Vinson.
The Ebola outbreak has killed about 4,500 people so far, mostly in Liberia, Guinea and Sierra Leone.
EU health ministers will meet in Brussels on Thursday to discuss the crisis, including the possibility of sending more troops to West Africa to help contain the virus.
Christopher Dye, WHO director of strategy, said the introduction of Ebola into the US or other countries in Western Europe was a matter “for very serious concern”.
“The possibility that once an infection has been introduced that it spreads elsewhere, is something that everybody is going to be concerned about,” he said.
But he added: “We’re confident that in North America and Western Europe where health systems are very strong, that we’re unlikely to see a major outbreak in any of those places.”
Earlier, President Barack Obama said the likelihood of a widespread Ebola outbreak was “very, very low”.
However, he promised a “much more aggressive” monitoring of Ebola cases in the US and reaffirmed plans to send a “SWAT team” of experts to any hospital that reported an infection.
Barack Obama cancelled a political campaign trip to chair a crisis meeting on Ebola on Wednesday and has cleared his diary for Thursday.
The president said it would be more difficult to prevent an outbreak in the US if the epidemic “rages out of control in West Africa”.
US health officials are facing new questions about the response to Ebola infections in Texas.
Liberian Thomas Eric Duncan was treated at the Texas Health Presbyterian Hospital but died of the disease.
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