His comments, clearly diverging from prime minister Tony Blair's consistent support for Mr Bush's policies, are likely to appeal to Labour grassroots activists in the forthcoming party campaign to succeed John Prescott.
Mr Benn explained that the global struggle against terrorism was not "us against one organised enemy with a clear identity and a coherent set of objectives".
"It is the vast majority of the people in the world - of all nationalities and all faiths - against a small number of loose, shifting and disparate groups who have relatively little in common apart from their identification with others who share their distorted view of the world and their idea of being part of something bigger," he said.
Mr Benn also restated the UK's support for the International Criminal Court, which Washington has historically resisted, as well as underscoring the importance of international development.
"I welcome the realisation that we are not engaged in a war with the various proponents of terrorism around the world," Dr John Sloboda of the Oxford Research Group thinktank said.
"But if we simply change words without a radical change in policy, nothing much has been achieved," he added.
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.