Obama is also requesting $400 million to upgrade security along the U.S.-Mexico border and to combat narcoterrorists.
Budget office spokesman Tom Gavin said the White House would send an official request to Congress late Thursday.
Robert Gibbs, the White House press secretary, acknowledged that Obama has been critical of Bush's use of similar special legislation to pay for the wars. He said it was needed this time because the money will be required by summer, before Congress is likely to complete its normal appropriations process.
"This will be the last supplemental for Iraq and Afghanistan.
The process by which this has been funded over the course of the past many years, the president has discussed and will change," Gibbs said.
The request is likely to win easy approval from the Democratic-controlled Congress, despite frustration among some liberals over the pace of troop withdrawals and Obama's plans for a large residual force of up to 50,000 troops - about one-third of the force now there - who will train Iraqis, protect U.S. assets and personnel and conduct anti-terror operations.
The outlines of the request were provided in documents presented at a closed-door congressional briefing.
According to the documents, obtained by The Associated Press, the request would fund an average force level in Iraq of 140,000 U.S. troops. It would also finance Obama's initiative to boost troop levels in Afghanistan to more than 60,000 from the current 39,000. And it would provide $2.2 billion to accelerate the Pentagon's plans to increase the overall size of the U.S. military, including a 547,400-person active-duty Army.
Some Democrats were not pleased.
"This funding will do two things - it will prolong our occupation of Iraq through at least the end of 2011, and it will deepen and expand our military presence in Afghanistan indefinitely," said anti-war Rep. Lynn Woolsey, D-Calif. "Instead of attempting to find military solutions to the problems we face in Iraq and Afghanistan, President Obama must fundamentally change the mission in both countries to focus on promoting reconciliation, economic development, humanitarian aid, and regional diplomatic efforts."
But House GOP Leader John Boehner of Ohio predicted Republicans would overwhelmingly support the request, provided congressional Democrats don't seek to "micromanage" the war by adding a timeline or other restrictions on the ability of military officials to carry on the fight.
Defense Secretary Robert Gates, a holdover from the Bush administration, said, "The reality is the alternative to the supplemental is a sudden and precipitous withdrawal of the United States from both places, and I don't know anybody who thinks that's a good idea." He said, "The reality is it would put everything we have achieved in Iraq at tremendous risk, and I believe it would greatly endanger our troops."
Obama was a harsh critic of the Iraq war as a presidential candidate, a stance that attracted support from the Democratic Party's liberal base and helped him secure his party's nomination.
He opposed an infusion of war funding in 2007 after Bush used a veto to force Congress to remove a withdrawal timeline from the $99 billion measure.
But he supported a war funding bill last year that also included about $25 billion for domestic programs. Obama also voted for war funding in 2006, before he announced his candidacy for president.
The upcoming request will include $75.8 billion for the military and more than $7 billion in foreign aid. Pakistan, a key ally in the fight against al-Qaida, will receive $400 million in aid to combat insurgents.
The upcoming debate in Congress is likely to provide an early test of Obama's efforts to remake the Pentagon and its much-criticized weapons procurement system. He is requesting four F-22 fighter jets costing about $600 million as part of the war funding package but wants to shut the F-22 program down after that.
The special measure would include $3.6 billion for the Afghanistan National Army.
The White House wants the bill for the president's signature by Memorial Day, said a House Democratic aide.
Obama announced plans in February to withdraw U.S. troops from Iraq on a 19-month timetable.
His new request would push the war money approved for 2009 to about $150 billion. The totals were $171 billion for 2007 and $188 billion for 2008, the year Bush increased the tempo of military operations in a generally successful effort to quell the Iraq insurgency.
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