"It's not looking promising", Trump said, but "I won't accept that he's dead".
"Today, with aching hearts, we are sharing devastating news about Robert Levinson, the head of our family".
Iranian officials have repeatedly said they had no information about Levinson.
"Our family also wishes to thank Congressman Ted Deutch, Senator Bill Nelson, Senator Marco Rubio and Senator Bob Menendez, and their staff members, who fought for Bob Levinson in every possible way.""Our family will spend the rest of our lives without the most wonderful man we have ever known, a new reality that is inconceivable to us". His grandchildren will never meet him.
"Those who are responsible for what happened to Bob Levinson, including those in the USA government who for many years repeatedly left him behind, will ultimately receive justice for what they have done", their statement said.
Mr Levinson disappeared in Iran 13 years ago from the island of Kish off Iran's southern coast.
At the time of the disclosure, his family said the US government failed to make his recovery the priority it should have been.
But The Washington Post reported in 2013 that Levinson, who had retired from the Federal Bureau of Investigation, was working for the CIA and had gone on a rogue mission aimed at gathering intelligence on Iran.
The Trump administration has made it a priority to seek the release of American hostages and prisoners detained overseas.
Levinson was the longest-held hostage in US history, and his family had fought for over a decade for his safe return, blaming the Iranian regime for his capture and imprisonment.
Former FBI agent Robert Levinson, who went missing in Iran in 2007, is believed to have died while in the custody of the Middle Eastern nation, his family said.
"Those who are responsible for what happened to Bob Levinson, including those in the USA government who for many years repeatedly left him behind, will ultimately receive justice for what they have done", the family said. "He was an American hero - a true patriot, and his compassion and kindness knew no bounds", the family said.
Levinson's relatives vowed they would continue to pursue justice, both from the United States officials who stonewalled them for years and the Iranian captors.
"He had some rough problems prior to his detainment or capture".
"He was a great gentleman", he said. And by the evening, the White House issued a new statement created to remove some of the uncertainty expressed by the president.
The family said information USA officials had received led them to conclude that he is dead. But even then, his whereabouts and fate were not known. He became the longest-held U.S. citizen in history in 2016. Though the development gave the family a burst of hope, Iran clarified that the "open case" was an investigation into his disappearance.