A major outbreak of Ebola in the US and elsewhere in the West is unlikely given the strong health systems, the World Health Organization (WHO) says.
US President Barack Obama also said the risk of Americans getting the virus was "extremely low", although he ordered a "much more aggressive response".
The US is investigating how a nurse infected when treating a victim in Texas was allowed to travel on a plane.
Officials are trying to trace the 132 people who flew with Amber Vinson.
The disease has killed about 4,500 people so far, mostly in Liberia, Guinea and Sierra Leone.
EU health ministers are meeting in Brussels to discuss the crisis, including increased screening of travellers and the possibility of sending more troops to West Africa to help contain the virus.
Meanwhile, US federal health officials will appear before a congressional committee on Thursday to answer questions about their handling of the crisis.
'Very low'
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 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.
Britain, Canada and the US have introduced increased screening of travellers arriving at airports from West Africa.
France said on Wednesday that it would begin checks from Saturday on passengers arriving at Paris Charles de Gaulle airport from the Guinean capital, Conakry.
Nurse allowed to travel
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.
Two nurses, Nina Pham and Amber Vinson, contracted Ebola after treating him.
Both wore face shields, hazardous materials suits and protective footwear as they drew blood and dealt with Mr Duncan's body fluids and it remains unclear how they were infected.
Ms Vinson later contacted the US Centers for Disease Control and Prevention (CDC) to inform it she was travelling on a plane on Monday - Frontier Airlines Flight 1143 from Cleveland to Dallas-Fort Worth.
She reported a temperature of 37.5C (99.5F).
CDC director Thomas Frieden said she should not have travelled on a commercial flight.
However, another health official told the New York Times later that Ms Vinson was not prevented from flying because the temperature was mildly elevated and was in a category not covered by the CDC.
"I don't think we actually said she could fly, but they didn't tell her she couldn't fly," the official told the Times. "She called us... I really think this one is on us."
Officials are trying to trace all 132 passengers but insist that as Ms Vinson did not have a fever, the risk to "any around that individual on the plane would have been extremely low".
Ms Vinson has now been transferred to Emory University hospital in Atlanta.
Mr Duncan, who was the first person to be diagnosed in the US with Ebola, started showing symptoms of the disease days after he arrived in Texas from Liberia.
Meanwhile, campaign group Avaaz said it had identified more than 2,000 international volunteers, including hundreds of doctors and nurses, who are willing to help fight the Ebola outbreak in West Africa.
The group said it would give the names to aid agencies working in the field but most are unlikely to arrive in the region in the near future because of the training needed before they can be deployed.
(BBC)