The decision has been made by the Australian Federal Police and the Commonwealth Director of Public Prosecution.
Morris Iemma and the state's police commissioner Ken Moroney want the federal authorities to review their decision.
The controversial books promote suicide bombings and anti-Australian conspiracies, but a ruling has been made that they don't breach sedition laws.
Mr Iemma says he hopes the Commonwealth will reconsider ways of prohibiting their sale.
"Whether it's a book or a manual or other material that is publicly available that gives people information on how to construct a bomb or a suicide bombing or some other form of terrorist act, it's a huge concern."