Abizaid told reporters in Iraq he wanted several thousand more troops, and indicated they may come from the 3rd Infantry Division, which only returned from its last Iraq deployment six months ago.
Pentagon officials said it was unlikely the 3rd ID would be called up so quickly.
The senior defense official said Abizaid's request was too specific for a warfighting commander to make. The forces Abizaid gets will be decided on by the Joint Staff in Washington. He is supposed to limit his requests to capabilities and Washington decides, based on scheduling and skills and equipment, how to fill those requirements.
Rumsfeld promised this week if Abizaid wanted more forces he would get them.
Whatever the military requirement, adding troops to the force in Iraq carries with it a poltical price. More than a year ago, then Army Chief of Staff Gen. Eric Shinseki told Congress the occupation of Iraq would require "several hundred thousand" troops. Deputy Defense Secretary Paul Wolfowitz called that estimate "wildly off the mark." The Pentagon leaked the name of Shinseki's replacement months before his scheduled retirement, rendering him a lame duck.
In his farewell speech at his retirement ceremony last year, Shinseki warned the Army was being over-committed.
"Beware the 12-division strategy for a 10-division Army," he said. "Our soldiers and families bear the risk and the hardship of carrying a mission load that exceeds what force capabilities we can sustain, so we must alleviate risk and hardship by our willingness to resource the mission requirements."
As Shinseki predicted, the Army is very heavily tapped. Between Iraq and Afghanistan, nine of its 10 divisions are either on deployment or have recently been relieved by other forces and are due for rest and retraining.
The U.S Marine Corps has tapped roughly 70,000 Marines for duty in Iraq next year alone. The senior defense official said Marines are likely to be called on to fill in the ranks because of the strain on the Army.
Abizaid asked his staff for options in Iraq earlier this week as violence in the country increased, sparked by a rebellious Shiite cleric and insurgent attacks on coalition forces. More than 200 U.S. personnel have been injured in combat in the last 24 hours, according to Defense Department statistics
Some fraction of the 1st Armored Division, due to rotate out of Iraq by May, could be forced to stay for another three months, Pentagon officials said. One officer with the division in Baghdad has already had his redeployment orders slowed, he told United Press International.
There are now 135,000 U.S. personnel in Iraq, some of who are overlapping as new forces rotate in to relieve others. The number of troops was supposed to drop to 105,000 by June. However, with increased violence and the potential for more as the June 30 hand over deadline nears, that target may be unrealistic.
Fighting in the last week has claimed at least 40 American soldiers and Marines. U.S. Central Command said Friday two soldiers and three Marines were killed April 8 and April 9. One soldier from the 13th Corps Support Command was killed and 12 injured in an attack on their convoy near Baghdad International Airport Friday. Also Friday, one 1st Cavalry Division soldier was killed and another wounded when they were ambushed as they responded to a mortar attack near their base.
Three Marines were killed April 8 in the restive Al Anbar province, the region that encompasses Falujah and Ramadi, where insurgents have stepped up operations.
There have been at least 458 U.S. forces killed in action Iraq as of Friday. A total of 3,269 have been wounded in combat since the war began more than a year ago.