The extra $33 billion in 2010 would mostly go toward the expansion of the war in Afghanistan. Obama ordered an extra 30,000 troops for that war as part of an overhaul of the war strategy late last year.

Military officials have suggested that the 2011 request would top $700 billion for the first time, but the precise figure has not been made public.

The administration also plans to tell Congress next month that its central military objectives for the next four years will include winning the current wars while preventing new ones and that its core missions will include both counterinsurgency and counterterrorism operations.

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