The spokesman declined to provide additional information, citing privacy considerations.
She said she is anxious about his health, because he has had cancer and suffers from asthma.
The imprisonment of Michael R. White, 46, of Imperial Beach, California, was reported by The New York Times earlier this week.
Joanne White told the New York Times that State Department officials had told her they were seeking access to her son via the Swiss consulate, as the USA does not have formal diplomatic ties with Iran.
The Swiss have provided consular services for Americans in Iran since 1980 when the USA cut off diplomatic ties with Tehran.
Tension between Iran and the United States has risen significantly since last May, when US President Donald Trump withdrew from an worldwide nuclear deal with Tehran and reimposed US sanctions that had been lifted after a 2015 accord.
Helicopter rescues injured skier in French Alps, dramatic video shows
Nicolas Derely wrote in a Facebook post that he was with his family skiing on January 2 when his son's friend injured his knee. A helicopter pilot showed off their incredible navigation skills when they rescued an injured skier in France last week.
She shortly filed a missing-person report with the State Department, prompting the Department of Homeland Security to contact her. She said she does not know the charges he's facing.
Washington has repeatedly called on Tehran to release American detainees, including Iranian-Americans Siamak Namazi and his father Baquer Namazi, Chinese-American Xiyue Wang, and Lebanese U.S. permanent resident Nizar Zakka. The son was held while visiting relatives in Tehran; both were sentenced in 2016 to 10 years in prison for what the Iranian government said was "cooperating with Iran's enemies", which usually implies cooperating with the United States. Xiyue Wang, a Chinese-born United States citizen and graduate student from Princeton University, was arrested in Iran in 2016. The Iranian government in 2017 said Wang was sentenced to 10 years in prison after being convicted of spying.
United States officials have also pushed Iran for information about the whereabouts of Robert Levinson, a former Federal Bureau of Investigation agent and Central Intelligence Agency contractor who went missing in Iran in 2007. USA officials believe Levinson, who suffered from diabetes, died in captivity after meeting with an American-born Islamic militant.
Former FBI agent Robert Levinson disappeared while visiting Iran's Kish Island in 2007.
White would join at least three other U.S. citizens, two of them of Iranian descent, in being detained in the country.
In January 2016, Iran freed four U.S. prisoners - Washington Post journalist Jason Rezaian, Marine veteran Amir Hekmati, Christian pastor Saeed Abedini and Nosratollah Khosravi-Roodsari - in exchange for the USA granting clemency to seven Iranians indicted or imprisoned in the United States.
The last time prisoners were released by the Iranian regime was after the nuclear accord took effect in 2016.
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