The money, mainly for the deployment of 30,000 additional troops to Afghanistan and other war costs in the current 2010 fiscal year, would come on top of Obama's expected request to increase the Pentagon's overall budget in fiscal 2011 to a record $708 billion, the officials said on condition of anonymity.
Fiscal 2010 Defence Department funding, including war costs in Afghanistan and Iraq as well as military construction, already comes to $660 billion.
If approved by Congress, the $33 billion emergency funding request, in line with estimates released last month by the Pentagon, would push that 2010 total to $693 billion.
The budget for fiscal 2011, which begins on October 1, is expected to be released by the White House on February 1.
The White House Office of Budget and Management declined to comment.
A Pentagon spokesman said: The president's 2011 budget request will be released by the administration on February 1 and it would be inappropriate to discuss details until then.
Despite the proposed increase for next year, analysts say Pentagon procurement is likely to remain under pressure, and more weapons-buying programs may be cut, because personnel and health care costs are eating up more and more of the overall Pentagon budget.
Last week, Admiral Mike Mullen, chairman of the Joint Chiefs of Staff, said he expected Pentagon funding to begin to drop within a couple years because of the country's economic woes.
High unemployment and a record $1.4 trillion deficit are among the toughest domestic challenges facing Obama and could dim the election prospects for his Democratic Party in congressional elections next November.But Obama and Defence Secretary Robert Gates face a major challenge trimming even a limited number of weapons programs over the objections of lawmakers who see them as a source of skilled manufacturing jobs.
Last year, Congress eliminated funding for Lockheed Martin Corp's F-22 fighter jet, as Obama had requested.
But lawmakers funded 10 more Boeing Co C-17 transport planes than the Pentagon had asked for, at a cost of $2.5 billion.
Congress also kept alive an alternate engine for the F-35 Joint Strike Fighter made by General Electric Co and Rolls Royce Group, despite Pentagon objections.
(Editing by Vicki Allen)