One of the experts leading America's fight against the coronavirus sounded a warning Wednesday that points to the possibility that international air travel may not fully open even when the number of new cases in the U.S. starts to fall.

Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said that in discussions with the World Health Organization, he learned the Chinese are concerned about new cases coming into their country even as the rate of infection has substantially fallen.

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China is where the coronavirus originated and the nation that has seen the most cases to date.

Though China has recently reported few new cases, per his Fauci's WHO conversations, "what they are starting to see as they are relaxing the constraints on travel is that they are getting imported cases."

Fauci said he was warned that when the U.S. gets control of domestic cases, officials should "very carefully examine how you are going to release the constraints."

President Donald Trump has imposed a travel ban on all foreign nationals into the U.S. from China, Iran and Europe. Last week, Trump closed the U.S. borders with Mexico and Canada to all but travel deemed essential. The European restrictions, announced March 11, were expected to last 30 days.

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Airlines have vastly reduced their international flights in response. United Airlines, for instance, said flights to foreign countries will be reduced by 90% in April.

Though they could be extended, travel restrictions are expected to ease as the coronavirus threat lets up in the U.S.

But with the world lacking a vaccine against the outbreak, Fauci cautioned about the need to guard against reinfection, though he made no specific recommendation.

"I know we're going to be successful in (getting) this under control, but I think we're going to have to remember, we don't want to import cases in," he said.

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