Al-Fidaa, which is used by the Al Qaeda to recruit suicide bombers, posted comments by one member, Abu Dujanah al-Kinani, warning that the "lion's cubs" are now waiting for the right time to avenge bin laden's death.
NBC News said the posts called for the Navy Seal's "destruction" in revenge for the al-Qaeda leader's killing.
"We pray to Allah for his destruction sooner rather than later," said one of the posts.
"Make an example of him for the whole world and give him dark days ahead," read another.
Among the websites publishing the death threats was the "Al-Fidaa" web forum, which the Al Qaeda uses to distribute its media and public communications, said Evan Kohlmann, an NBC News consultant and a terrorism analyst at Flashpoint Partners, a global security firm.
Ex-SEAL's former commander, special operations chief Admiral Bill McRaven warned his troops, both current and former, that he would take legal action against anyone found to have exposed sensitive information that could cause fellow forces harm.
The news of the book release had taken the United States government and military by surprise with senior officials saying Bissonnette had not sought approval for the contents of the book and neither got the book vetted before releasing it.
"We will pursue every option available to hold members accountable, including criminal prosecution where appropriate," McRaven wrote in an open, unclassified letter emailed to the active-duty special operations community Thursday.
The author of No Easy Day is slated to appear in disguise on the CBS News programme 60 Minutes on September 9.
Penguin Group's Dutton imprint, the publisher, asked news organisations to withhold his identity.
"Sharing the true story of his personal experience in No Easy Day is a courageous act in the face of obvious risks to his personal security," Dutton spokeswoman Christine Ball said in a statement.
"That personal security is the sole reason the book is being published under a pseudonym."
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