Nizar Zakka, 50, was rushed to a hospital on Sunday, where he refused an IV, his brother Ziad told The Associated Press. He said his brother is prepared to die if he is not released, and refused to sign documents in Farsi, a language he doesn't understand.
Zakka, who has permanent US residency, went missing on Sept. 18, 2015, during his fifth trip to Iran. Two weeks later, Iranian state TV reported that he was in custody and suspected of "deep links" with US intelligence services.
It showed what it described as an incriminating photo of Zakka and three other men in army-style uniforms, two with flags and two with rifles on their shoulders. But the photo was actually from a homecoming event at Zakka's prep school, the Riverside Military Academy in Georgia, according to the school's president and his brother.
Last September, Zakka was sentenced to 10 years in prison and handed a $4.2 million fine after being convicted of espionage by a security court.
Zakka's family denies the allegations.
His brother said he had been invited to attend a conference at which President Hassan Rouhani spoke of sustainable development and providing more economic opportunities for women. He showed the AP a letter of invitation for his brother from Iranian Vice President Shahindokht Molaverdi.
"He is completely losing hope in life, and this is the most difficult period a human being might reach," Zakka said in an interview in Beirut, adding that he had urged his brother to end the hunger strike when he spoke to him by phone early on Tuesday.
The family has urged Lebanese President Michel Aoun to raise Zakka's case when he visits Iran in August. Aoun is a close ally of Hizballah, a powerful Iranian-backed Lebanese group.
"We hope that President Aoun will reach a happy ending in this matter," said Majed Dimashkiyeh, a lawyer for the family who has sent an official letter to Aoun asking him to intervene with Iranian authorities.
Ziad Zakka said their mother passed away last July. He said she had sent a letter to Iran's Supreme leader Ayatollah Ali Khamenei and Rouhani through the Iranian Embassy in Beirut, telling them that "my dream is to see Nizar."
Zakka, who used to live in Washington, leads the Arab ICT Organisation, or IJMA3, an industry consortium from 13 countries that advocates for information technology in the region.
The Associated Press reported in May last year that IJMA3 had received at least $730,000 in contracts and grants since 2009 from both the State Department and the US Agency for International Development, USAID.