HAVANA — Thousands of Cubans have had their travel plans thrown into limbo by the U.S. State Department’s announcement Friday that it was indefinitely suspending visa processing in Cuba. The move was attributed to a roughly 60 percent reduction in embassy staffing after 21 diplomats were left with serious health problems by mysterious attacks that have yet to be fully explained.

On the first business day since the announcement, about 300 people milled about in what is known as the “park of laments,” a small plaza near the embassy where visa-seekers wait for appointments.

Associated Press journalists spoke to about a dozen people there, all of whom worried that families separated by the 90 miles of the Florida Straits stand to suffer the most.

“My mother cried on the phone when we talked Friday,” said Carlos Sierra, a 31-year-old restaurant worker whose hopes for a family reunification visa to join his parents in the United States are now on hold.

He had hoped to find a job there and send money back to his wife and 6-year-old son. “For now,” Sierra said, shaking his head, “the only thing I can do is wait.”

The U.S. government also issued a travel warning for the island, potentially threatening tourism by Americans following a nearly three-year-old, partial thawing of relations that have been icy since the Cold War.

Cuba’s government has criticized the U.S. response as “hasty” and expressed regret it was implemented before investigations yield conclusive results about the attacks. President Raul Castro’s government has denied responsibility.

U.S. officials have not identified whatever device might be responsible. They have pointedly not accused Cuba’s government directly of culpability, while criticizing it for failing to protect foreign diplomats on its soil.

About 2 million people of Cuban origin live in the United States, and just about everyone on the island has some family connection to the country.