It was the first time the Swiss had been able to see Mr. White since he was seized in Mashhad last July and taken to Vakilabad Prison, after having visited a person his family has described as an Iranian girlfriend. He has still not been able to communicate directly with his family.

Mr. White, 47, of Imperial Beach, Calif., served in the Navy for 13 years. He is the first American to be incarcerated in Iran since President Trump took office in 2017, adding a complication to what already was a severely strained relationship between the United States and Iran.

He is one of at least four Americans known to be held in Iran, where the government has regarded the United States as its top enemy since the Islamic revolution that overthrew the shah 40 years ago.

“Over the past few weeks,” Ms. White said, “I’ve learned that Mike was badly beaten when he was arrested and that he has been taken to court at least twice for proceedings in Farsi that he couldn’t understand. My son is not well. His health is deteriorating, and I want him back so I can get him the care he badly needs.”

Alireza Miryousefi, a spokesman for Iran’s United Nations Mission, confirmed in an email that the Swiss had met with Mr. White and that another meeting was planned in “coming days.”