Critics have said that the warning went unheeded by US President George Bush until the 11 September 2001 attacks.
The memo dated 25 January 2001 - five days after Bush took office - was an essential feature of last year's hearings into intelligence failures before the attacks on New York and Washington.
A copy of the document was posted on the National Security Archive website on Thursday.
The memo, from former counterterrorism chief Richard Clarke to then-national security adviser Condoleezza Rice, had been described during the hearings but its full contents had not been disclosed.
Clarke, a holdover from Bill Clinton's administration, had requested an immediate meeting of top national security officials as soon as possible after Bush took office to discuss combating al-Qaida.
He described the network as a threat with broad reach.
Al-Qaida's Asian threat
"Al-Qaida affects centrally our policies on Pakistan, Afghanistan, Central Asia, North Africa and the GCC [Gulf Arab states]. Leaders in Jordan and Saudi Arabia see al-Qaida as a direct threat to them," Clarke wrote.
Rice (L) was warned of al-Qaida's
threat when she first took office
"The strength of the network of organisations limits the scope of support friendly Arab regimes can give to a range of US policies, including Iraq policy and the [Israeli-Palestinian] peace process. We would make a major error if we underestimated the challenge al-Qaida poses."
The memo also warned of overestimating the stability of moderate regional allies threatened by al-Qaida.
It recommended that the new administration urgently discuss the al-Qaida network, including the magnitude of the threat it posed and strategy for dealing with it.
The document was declassified on 7 April 2004, one day before Rice's testimony before the September 11 commission.
It was released recently by the National Security Council to the National Security Archive - a private library of declassified US documents obtained through the Freedom of Information Act.
The meeting on al-Qaida requested by Clarke did not take place until 4 September 2001, one week before 9/11.