Former Navy Seal Matt Bissonette, who uses the pseudonym Mark Owen, was interviewed by CBS television network.
He repeated his claim that Osama Bin Laden was shot as soon as he looked out of his bedroom, contrary to the official version of events.
The Pentagon has said it may sue Matt Bissonette for divulging military secrets.
In the interview, Matt Bissonnette defended what he said was the manner of Osama Bin Laden’s death.
“If a guy sticks his head around the corner he very easily could have a gun,” he told CBS’ 60 Minutes programme.
“You don’t wait to get that AK or the grenade thrown down the hall or the suicide vest,” he added.
He said that Osama Bin Laden was still moving after the first shot and was shot again when the Seals entered the room.
“[The Seals] couldn’t see his hands. So, he could’ve had something. Could’ve had a hand grenade or something underneath his chest,” Mark Owen said.
US officials had stated he was shot only after he had ducked back into the bedroom, prompting fears he might be grabbing a weapon.
Matt Bissonette told of a later meeting with President Barack Obama at which the Navy Seals refused to tell him which of them had shot Osama Bin Laden.
“Pulling a trigger is easy…. It’s not about who that one person was, it’s about the team… that teed this whole thing up,” Matt Bissonette said.
“Who cares who the one person is. Doesn’t matter,” he added.
The book was not reviewed ahead of publication by the Pentagon, CIA or the White House – and officials had warned that criminal charges could result from the improper disclosure of secret information.
The Pentagon’s general counsel, Jeh Johnson, has written to the author to inform him that “in the judgment of the Department of Defense, you are in material breach and violation of the non-disclosure agreements you signed.”
The Pentagon is considering “all remedies legally available to us”, the letter added.
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