"That's my understanding," Esper said in an interview late Wednesday with Fox News, when asked if Hamza bin Laden was dead.
"I don't have the details on that. And if I did I'm not sure how much I could share with you," he added.
US media reported at the beginning of August that bin Laden was killed during the last two years in an operation that involved the United States, citing US intelligence officials.
But President Donald Trump and other senior officials have refused to confirm or deny it publicly.
"I don't want to comment on it," Trump told reporters when asked.
The 15th of bin Laden's 20 children and a son of his third wife, Hamza, thought to be about 30 years old, was "emerging as a leader in the al Qaeda franchise," the State Department said in announcing the reward.
His father's death in 2011 and the rise of the more virulent Islamic State group saw al Qaeda lose currency with younger militants, but the group appears to have been plotting a stealthy comeback under leader Aymanal Zawahiri.
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