Levinson, who worked as a private investigator after retiring from the agency, disappeared in 2007 while on Kish Island in the Persian Gulf. Family members said he was going to Iran to investigate cigarette smuggling for a private client, the newspaper reported Friday.
The video, received by the family in Nov. 2010, shows him sitting in a makeshift cell. He said on the tape that he had been held by his unidentified captors for more than three years.
"I need the help of the United States government to answer the requests of the group that has held me," he said on the tape. "Please help me get home. Thirty-three years of service to the United States deserves something."
Footage from the videotape was posted on the Levinson family's Web site, where his wife, Christine, and one of the couple's children are also seen appealing for his release.
The video was not previously released due to ongoing investigations, the FBI said. "The investigation to locate Mr. Levinson continues, as the U.S. government continues to work to find him and bring him home safely," FBI spokeswoman Jacqueline Maguire said in a statement, the Times said.