In that letter, Bush wrote that “acting pursuant to the Constitution and Public Law 107-243 [the Iraq war resolution] is consistent with the United States and other countries continuing to take the necessary actions against international terrorists and terrorist organizations, including those nations, organizations, or persons who planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001.”
The letter starts by announcing that it has been sent in conformity with the war resolution’s section 3b, which asks that the president make a determination that (among other things) the use of force against Iraq is consistent with continuing to take the necessary actions against the 9/11 plotters.
It is by no means obvious to me that saying that fighting Iraq is “consistent with continuing” to fight the 9/11 plotters amounts to saying that fighting Iraq is part of the project of fighting those plotters. The more natural construction (or so it seems to me) is that the second fight doesn’t conflict with the first. That is, Congress authorized Bush to use force against Iraq if he determined that it would not hurt the fight against al Qaeda, and he determined that it would not. I’ll admit that the language is not particularly clear.