President Trump’s order that the United States exit the World Health Organization could undo programs meant to ensure the safety, security and study of a deadly virus that once took half a billion lives, experts warn. His retreat, they add, could end decades in which the agency directed the management of smallpox virus remnants in an American-held cache.

Health experts say discontinuation of the W.H.O.’s oversight threatens to damage precautions against the virus leaking into the world, and to disrupt research on countermeasures against the lethal disease. They add that it could also raise fears among allies and adversaries that the United States, under a veil of secrecy, might weaponize the smallpox virus.

“I’ve been in that lab,” said Thomas R. Frieden, a former director of the Centers for Disease Control and Prevention in Atlanta, where the American cache resides. “Imagine a submarine inside a building and the people walking around in spacesuits. It looks like something out of a movie.” To reduce smallpox risks and misperceptions, Dr. Frieden added, “we need to open ourselves up to inspection.”

On Monday, Daniel R. Lucey, a Dartmouth medical professor, posted an article on the blog of the Infectious Diseases Society of America warning that Mr. Trump’s W.H.O. exit could imperil “smallpox virus storage, experiments, reporting and inspections.”

A half century ago, the W.H.O. purged the smallpox virus from human populations after the scourge had killed people for thousands of years. Dr. Frieden called it “one of the greatest accomplishments not just of medical science but global collaboration.”

While the germ was eradicated in people, two repositories were preserved to allow study of the virus should it re-emerge: one in Atlanta, the other in Russia. To curb leaks, both caches are stored in special labs classified as Biosafety Level 4, the highest tier of protection.