The number of American troops taken to Germany for further evaluation and treatment also increased, to 18 from 17, according to the Pentagon’s statement Tuesday.

One service member who was taken to Kuwait has since returned to duty, Colonel Campbell said.

Brain injuries are not always immediately apparent, officials have said, noting that delays in reporting the injuries can also be caused by the time it takes for information to work its way to leaders in Washington.

The rising number of injuries undercuts Mr. Trump’s initial statements hours after the strike, in which he said that no Americans were hurt.

“I’m pleased to inform you the American people should be extremely grateful and happy,” the president said in a speech on Jan. 9. “No Americans were harmed in last night’s attack by the Iranian regime.”

After the Pentagon said that American troops were showing signs of concussions after the Iranian missile strikes, Mr. Trump on Jan. 22 disregarded the symptoms as “not very serious,” drawing criticism from veterans’ groups.