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.
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.