Admiral Mullen’s spokesman, Capt. John Kirby, said afterward that although the admiral wanted to move away from supplemental defense financing, there might be “a need for another supplemental on the unique and current demands of dynamic operations in two theaters of war.”

The White House had little comment on Admiral Mullen’s remarks. “The president’s budget provides a full-year funding for anticipated costs in Iraq and Afghanistan, and he has made clear his intent to fund these wars through the normal budgeting process,” Tommy Vietor, a White House spokesman, said in an e-mail message. “No decisions have been made about additional costs related to new resource requests from the Department of Defense.”

Although the size of any request would depend on the number of extra forces sent, Defense Department officials say they are likely to need more money even without a buildup. Robert F. Hale, the Pentagon comptroller, recently told staff members of the House Appropriations Committee that it would be hard to get through September 2010 with $130 billion, regardless of a troop increase, said a Congressional staff member who did not want to be identified as discussing internal matters. Mr. Hale declined to comment.

In March, Mr. Hale told the House Budget Committee that $130 billion would be enough for the year and that he did not expect to ask for more. But he did caution that “there may be significant unforeseen developments or changes in wartime strategy or tactics that cannot be addressed with existing resources.”

Mr. Obama did include the $130 billion for the wars as part of his regular $668 billion defense budget this year, the first time that has happened since 2001. President George W. Bush regularly financed the wars with emergency requests that usually came after the Pentagon budget was introduced.

In April, before the current Pentagon budget was passed, the Obama administration asked Congress for approval of an emergency $83.4 billion to pay for the wars in Iraq and Afghanistan through Sept. 30. The administration said the money was needed because legislation passed during the Bush administration provided only enough money to pay for the wars through midyear.

Robert Gibbs, the White House press secretary, said at the time that the request was unavoidable and that it would be the last outside the normal budget process.