General Petraeus has agreed to the cut from 15 to 14 combat brigades, but not until February.
The US currently has about 146,000 troops in Iraq, including 15 combat brigades and thousands of support forces.
US military officials are increasingly worried about escalating conflict in Afghanistan.
US military officials are worried over escalating fighting in Afghanistan [AFP]
An unnamed senior official said it was critical to start replacing the marines in Afghanistan soon.
"We believe the risk in Afghanistan is such that we need to do something, and the risk in Iraq is such that we can go into Afghanistan without risking unduly the posture in Iraq," the official said.
Bush, whose term ends in January, is expected to announce his next move before Robert Gates, the US defence secretary, and Admiral Mike Mullen, the chairman of the Joint Chiefs of Staff, testify before congress about Iraq and Afghanistan on Wednesday.
"The president is now considering his options," Dana Perino, a White House spokeswoman, said on Thursday.
Pentagon leaders have struggled to balance the two war fronts, repeatedly stressing that Iraq is the priority while calling the Afghanistan effort an economy-of-force operation.
On several occasions Mullen has said "in Afghanistan, we do what we can; in Iraq, we do what we must".
But decisions on any large-scale withdrawal from Iraq is expected to fall to Bush's successor.
The Democratic and Republican presidential nominees, Barack Obama and John McCain, have said that more troops are needed in Afghanistan.
The Iraq war is deeply unpopular with Americans although it has somewhat faded as an election issue with the decline in violence and increasing economic troubles at home.
Meanwhile, army officials on Thursday revealed that the suicide rate among US soldiers could surpass last year's record, and urged military leaders to increase prevention efforts.
|The US military is suffering the pressure of fighting two wars [Reuters]
There were 62 confirmed suicides among active duty soldiers and army reserves called to active duty this year, while another 31 deaths that appear to be suicides were being investigated.
There were 115 suicides last year.
Colonel Eddie Stephens, deputy director of human resources policy at the Pentagon, said this year's rate per 100,000, if all deaths are confirmed as suicides, would exceed that of civilian suicides.
"Installations and units across the army have been directed to redouble their efforts in awareness and prevention training and soldier care and support services."
Pete Geren, the army secretary, said in a statement over the weekend that "army leaders are fully aware that repeated deployments have led to increased distress and anxiety for both soldiers and their families".
"The army is committed to ensuring that all soldiers and their families receive the behavioural health care they need."