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".
- A "site manager" will supervise how workers at the Texas Health Presbyterian Hospital put on and take off protective clothing
- Two nurses from Emory University Hospital in Atlanta will offer "enhanced training" in Dallas
- An immediate response team will travel to the site of any future Ebola diagnoses to hit the ground "within hours"
- New guidelines for testing at hospitals throughout the US, with special emphasis on asking questions about travel history
However, he promised a "much more aggressive" monitoring of Ebola cases in the US.
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.
Amber Vinson was not supposed to travel on an aeroplane, health officials said
The disease has killed about 4,500 people so far, mostly in Liberia, Guinea and Sierra Leone
The UK's 22 Field Hospital prepares to fly out to Sierra LeoneTwo 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.
- The New York Times says the appearance of the latest Ebola patient "provided more signs of concern about federal officials' ability to control the spread of the disease... and indications that the issue was becoming politicised"
- A report by USA Today says health officials now believe Ebola patients should be treated at four specially designed US clinics rather than at hospitals around the country
- Ebola is becoming "the next great American panic", writes Chico Harlanin the Washington Post
- The Christian Science Monitor looks at how much large donations, such as the $25m (£16m) given by Facebook chief executive Mark Zuckerberg and his wife, Priscilla Chan, can help fight the spread of the disease
"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".
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.
Ebola patients treated outside West Africa*
*In all but three cases the patient was infected with Ebola while in West Africa. Infection outside Africa has been restricted to health workers in Madrid and in Dallas. DR Congo has also reported a separate outbreak of an unrelated strain of Ebola.Avoid direct contact with sick patients as the virus is spread through contaminated body fluids
