New way forward: We're gonna speak to their hopes, not their fears (2nd paragraph)
The US president has instead replaced it with a softer approach stressing "new partnerships" and multilateral diplomacy.
"Our long-term security will not come from our ability to instill fear in other peoples but through our capacity to speak to their hopes," Mr Obama said in a message introducing a new national security strategy.
In the 52-page document, drawn up after 16 months of deliberations, Mr Obama outlines a much broader set of priorities and methods than Mr Bush's tightly-focused determination to eradicate Islamism by any means possible and alone if necessary.
"We will always seek to delegitimise the use of terrorism and to isolate those who carry it out," it states. "Yet this is not a global war against a tactic – terrorism – or a religion – Islam.