He was the longest-held hostage in USA history.
Levinson, then a private investigator, was seeking information on alleged corruption involving former Iranian President Akbar Hashemi Rafsanjani and his family, sources familiar with his work said.
At the time of the disclosure, his family said the US government failed to make his recovery the priority it should have been.
In a statement on Wednesday, the Levinson family said it had recently received information from U.S. officials that had led them to draw their conclusion.
"We do not even know when, or even when, his physique can be returned to us. I am running very quickly out of diabetes medicine", he said in the recording. "We don't know when or how he died, only that it was prior to the COVID-19 pandemic", they said in a statement.
Levinson traveled to Kish Island, Iran, in early March 2007, according to State Department officials, and was never publicly seen or heard from again.
Months after he disappeared, USA government sources acknowledged that before traveling to Kish Island, Mr Levinson had maintained an unorthodox contractual relationship with the analytical branch of the Central Intelligence Agency.
Upon his arrival, Levinson was said to have met with an American fugitive - Dawud Salahuddin - targeted by the Central Intelligence Agency for recruitment, a source close to the Levinson case told Fox News in 2016.
"If not for the cruel, heartless actions of the Iranian regime, Robert Levinson would be alive and home with us today", the family said in their statement, noting that they have spent "13 years waiting for answers". "Our family will spend the rest of our lives without the most fantastic man, a new reality that is inconceivable to us".
The FBI Agents Association, which represents more than 14,000 active and former agents, said it would "not forget Bob and will support all efforts to bring to justice those responsible for this horrific crime".
Iranian officials have repeatedly said they had no information about him.
The family received a video in late 2010 as well as proof-of-life photographs in 2011 in which he appeared dishevelled with a long beard and wearing an orange prison jumpsuit like those given to detainees at the Guantanamo Bay prison.
The footage raised hypothesis that he might have been held by extremists in Pakistan, however U.S. officers later discounted the chance.
"I won't accept that he's dead", Trump told journalists after the family's announcement, adding that it wasn't "looking great". "They will know him only through the stories we tell them".
Senator Bob Menendez, who employs one of Levinson's sons on his staff, sounded more definitive on his death and vowed to hold Iran accountable.
Trump, who as a candidate had accused his predecessor Barack Obama of not doing sufficient for Levinson in negotiations with Iran, famous that the previous agent had longstanding well being issues. For years, the U.S. had masked his undercover mission, saying he was a private citizen in Iran on business. Thirteen years since we last saw him or had any contact with him.
Iran continues to be holding twin United States nationals Siamak Namazi, who was convicted in 2016 of fees that embody espionage and collaboration with the U.S. authorities, his father Baquer and environmental skilled Morad Tahbaz.