WASHINGTON — At least 16 Americans working at the U.S. Embassy in Havana became ill last year in a mysterious health attack, the State Department disclosed on Thursday.

The attack, which may have been caused by a sonic wave machine, seemed to begin last December. But American officials did not notice a pattern to the symptoms reported by employees until two months later.

“It took some time for people to be able to determine that, yes, there is a pattern taking place here. Yes, there is something going on,” said Heather Nauert, the State Department’s spokeswoman.

Once a pattern was seen, she said, the government responded fully.

“We take this situation extremely seriously,” Ms. Nauert said. She was careful not to blame the Cuban government.