The officials said the omission was justified because they had no way to know exactly how much money would be needed. But Democrats criticized the omission, saying it led to a significant understatement of the likely deficit and masked the financial and political costs of the missions.
"This budget attempts to hide the true cost of operations in Iraq and Afghanistan by delaying funding on all known and necessary costs of the war until a supplemental appropriation can be approved next year," said Senator Jack Reed, a Rhode Island Democrat who is on the Armed Services Committee.
Senator Edward M. Kennedy, Democrat of Massachusetts, said the administration should "level with the American people about the true costs" of operations in Iraq and Afghanistan.
The president's proposal is in keeping with recent practice. In November, Congress approved $87.5 billion for Iraq and Afghanistan, including $65.8 billion for military operations there in the 2004 fiscal year. That followed a supplemental spending package of $78.5 billion, which was approved last April and included $62.4 billion for the fighting in Iraq and Afghanistan and related military needs in the 2003 fiscal year.
The president's 2005 budget includes no such amounts. "It's not appropriate to put a number in there because we don't know what it's going to be," said Joshua B. Bolten, director of the White House Office of Management and Budget. "It's going to be requested in supplemental funding."
Mr. Bolten said that $50 billion was "the upper limit for what might be needed" for military operations in Iraq and Afghanistan in the 2005 fiscal year, which begins in eight months.
The budget director said Mr. Bush would request the additional money for Iraq next year, "when there's a clearer picture of what the security needs will be." The administration does not expect Congress to offset the additional spending.
"When you're fighting a war, it's hard to come up with cuts that can match that," Mr. Bolten said.
For more than a decade, Republican and Democratic administrations have financed wars and peacekeeping operations largely by asking Congress to reimburse the Pentagon for costs incurred after the fact.
This practice of requesting a supplemental appropriation came after Congress generally refused to create a separate military contingency fund, fearing that establishing such a discretionary pot of money would erode Congress's power of the purse.
In the late 1990's, however, Congress established the Defense Emergency Response Fund, which allowed the Pentagon to budget every year for missions that had become predictable, such as peacekeeping in the Balkans and flying patrols over northern and southern Iraq.
Administration officials argue that the operations in Iraq and Afghanistan are too unpredictable to consider financing in the regular budget. Pentagon officials are planning to field about 110,000 troops in Iraq and about 10,000 troops in Afghanistan this year. But in Iraq especially, they are hoping to reduce that number as more Iraqis take over security functions around the country.
Representative John M. Spratt Jr. of South Carolina, the senior Democrat on the House Budget Committee, said the administration should have included some money for military operations in Iraq because it was certain the cost would be more than zero. "We can do a rough calculation of the likely costs," Mr. Spratt said in an interview. "Administration officials should do that themselves and send us an approximation of the cost."
Senator Kent Conrad of North Dakota, the senior Democrat on the Senate Budget Committee, said the omission was one of many examples of "funny money accounting" in the president's budget request. "He's not telling the American people the real state of our fiscal condition," Mr. Conrad said.
Senator Robert C. Byrd, the senior Democrat on the Senate Appropriations Committee, said the repeated use of supplemental spending bills was a deceitful tactic that hid the true costs of American operations in Iraq and Afghanistan. "The administration views Congress like an automatic teller machine," Mr. Byrd said. "Just put the request in the A.T.M., and the money slides out in seconds, no questions asked."
Over all, the president's budget shows the deficit rising to $521 billion in 2004, from $375 billion last year, and he predicts it will decline to $364 billion next year.
But Mr. Bolten said the number for 2005 "does not include spending for our ongoing operations in Iraq and Afghanistan." Accordingly, he said, "we will need supplemental funding to continue that."
The military budget the Bush administration proposed on Monday seeks a major increase in missile defenses, holds steady on money to buy new weapons systems, and increases spending on personnel.
The $401.7 billion for the fiscal year beginning Oct. 1, represents a 7 percent increase over current spending, but proposes no big changes in major weapons systems or sharp departures from Defense Secretary Donald H. Rumsfeld's goal to revamp the military into a more agile, yet still lethal, fighting force.
"I don't expect it to be a very controversial budget this year," said Steven M. Kosiak, director of budget studies at the Center for Strategic and Budgetary Assessment, a research group. "It doesn't require making any hard choices, which may be required by the end of the decade."
One contentious area could be the administration's request for missile defenses. The request for the Missile Defense Agency is $9.2 billion, about 20 percent higher than this year's $7.6 billion.
The Pentagon's goal is to have the first 10 long-range interceptors operating by the end of this year six at Fort Greely, Alaska, and four at Vandenberg Air Force Base in California. A larger system of 20 ground-based missile interceptors and 10 sea-based interceptors would be in place by the end of 2005.
The proposed budget would finance immediate needs, like more armored Humvees, remotely piloted reconnaissance aircraft and advanced ships, as well as longer-range equipment, like a laser-based communications network and a new Army combat system.
The administration is also seeking up to $500 million to train and equip military and security forces in Iraq and Afghanistan, and neighboring friendly nations. This would expand on existing programs, that Pentagon officials said had been particularly useful in Afghanistan.
"We were able to take raw recruits, who couldn't even crawl on the ground and keep their helmets on at the same time, into a sophisticated force that operates alongside us and that creates a very positive image for the central government of Afghanistan," Dov S. Zakheim, the Pentagon comptroller said at a news conference on Monday.