The report by the Government Accountability Office released on Wednesday said the shortfall is forcing the Defence Department to shift funds from other uses, including pushing expenses from the 2004 fiscal into 2005.
"Analysis ... suggests that anticipated costs will exceed the supplemental funding provided for the war by $12.3 billion for the current fiscal year," the report said.
Congress approved an $87bn emergency spending bill in October 2003 to finance military operations in Iraq and Afghanistan through to the end of September.
Democrats estimate that the Pentagon has $5bn left to fund the 2004 shortfall but will need to find $7bn to cover it in the last two months of the fiscal year.
"The administration has failed to budget for the war in Iraq and Afghanistan," said top Democrat on the House Budget Committee, John Spratt.
"The time is long past for the administration to present a full accounting of the cost of the war and to ask Congress to put up the resources needed to fund it."
The report warned that deferring activities planned for the 2004 fiscal year "adds to the requirements that will need to be funded in fiscal year 2005 and potentially later years and could result in a 'bow wave' effect in future fiscal years".
It also criticised the Department of Defence for lack of transparency into how the money it was sent by Congress has been spent. The report said "large amounts" of funds were classified as miscellaneous, providing "little insight" into where the money went.