The Iranian government has never admitted abducting Mr. Levinson, who would have turned 72 this month. On March 9, the anniversary of his disappearance, the F.B.I. said: “During the past 13 years, the only credible evidence of responsibility in Mr. Levinson’s disappearance has pointed to those working for the government of Iran.”

The family thanked the C.I.A. director, Gina Haspel; the F.B.I. director, Christopher A. Wray; and Robert C. O’Brien, the national security adviser, in its statement. They were all in the White House meeting when the family was told, the person said.

In a statement, Mr. O’Brien called on Iran to “release all Americans who remain wrongfully detained in that country.”

“As President Trump said today, Iran must provide a complete accounting of what occurred with Bob Levinson before the United States can fully accept what happened in this case,” he said. “While the investigation is ongoing, we believe that Bob Levinson may have passed away some time ago.”

After retiring from the F.B.I. as a veteran investigator of drug cartels and organized crime, Mr. Levinson began working with C.I.A. analysts in a highly unusual arrangement. Though they had no authority to run spy operations, they paid him to gather intelligence, including on the Iranian government.

Mr. Levinson disappeared from Kish Island, off the coast of Iran, on March 9, 2007. He had traveled to Kish to investigate corruption and was trying to renew his C.I.A. contract.

After he disappeared, the C.IA. played down any relationship with Mr. Levinson and said he was not a current employee. For years, United States officials would only say that Mr. Levinson was working for a private firm on his trip when he vanished.