The memo said if a government employee were to torture a suspect in captivity, "he would be doing so in order to prevent further attacks on the United States by the al-Qaida terrorist network", the newspaper reported.
The memo also said that arguments centring on "necessity and self-defence could provide justifications that would eliminate any criminal liability" later, according to the Post.
The view from the Justice Department's office of legal counsel - written in response to a CIA request for legal guidance - was contained in a 50-page document obtained by the newspaper.
It cites government officials familiar with the document as saying that it was offered after the CIA began interrogating suspected al-Qaida leaders following the September 11 attacks.
The legal reasoning in the 2002 memo, which covered treatment of al-Qaida detainees in CIA custody, was used in a March 2003 report by Pentagon lawyers assessing interrogation rules for the US detention centre at Guantanamo Bay, Cuba, the Post said.
Bush administration officials say that, despite the discussion of legal issues in the two memos, the United States has abided by international conventions barring torture.
"The president directed the military to treat al-Qaida and Taliban humanely and consistent with the Geneva Conventions," a spokesman for the White House counsel's office told the Post.
On Monday, The Wall Street Journal said a classified Pentagon report on interrogation methods concluded that the president was not bound by laws prohibiting torture.
That report, compiled by military lawyers, came after commanders at Guantanamo Bay complained in late 2002 that they were not getting enough information from prisoners using conventional methods, the Journal reported.