It was grim, unsettling news: the United States warned Americans on Friday not to travel to Cuba and ordered the withdrawal of more than half its diplomats in Havana.

The announcement, which spread around the island in spurts, largely by word of mouth, dealt a harsh blow to Cubans who had hoped the nascent normalization of relations with the United States that began in late 2014 would usher in a period of economic growth and greater prosperity in the impoverished Communist nation.

“It’s a shame that they continue to throw up obstacles preventing two countries that are so close to engage culturally,” said Yaylen Vilches, 26, the manager of El Dandy, one of Havana’s most popular private restaurants. “This doesn’t just hurt us; they’re hurting people in both countries.”

The measures announced Friday — taken in response to hearing loss and other ailments that American government employees in Cuba had experienced in recent months — stirred anxiety and dread on the island.