The officer, who spoke to The Associated Press only on condition that he not be identified, said Petraeus was still analyzing the situation and had not yet submitted a final set of recommendations. That is expected to happen within the next week or so, but there is no firm deadline.
The officer would not provide any specifics of Petraeus' initial recommendation. He was granted anonymity because of the sensitivity of Petraeus' deliberations and because they are not completed.
Petraeus is widely expected to conclude that the outlook in Iraq - politically as well as militarily - has brightened enough in recent months to merit more troop cuts this fall. At Petraeus' recommendation, President Bush halted the drawdown when the last of five Army brigades, sent in 2007 as reinforcements, pulled out in mid-July; Petraeus wanted time to analyze the impact of losing those five brigades.
His recommendations to Gates and to Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, on how to proceed this fall will go to Bush for a final decision, likely in September.
Estimates of how deeply Petraeus would suggest cutting this autumn have generally ranged from one to two combat brigades, or roughly 3,500 to 7,000 troops. But some recent developments might argue for smaller reductions. That includes the unanticipated pullout of Georgian troops following the invasion of their country by Russia and a delay in holding Iraqi provincial elections.
There currently are 15 combat brigades in Iraq and a total of 146,000 troops, including tens of thousands that perform support, rather than direct combat, functions.
U.S. and Iraqi officials are working on a security agreement that would include at least a notional timeline for phasing out U.S. forces, to include a pullback of combat troops from Iraqi cities by June 2009 and a broader withdrawal by the end of 2011. That is separate from Petraeus' recommendations to Gates, which are thought to be focused more on shorter-term reductions.
Petraeus, along with his soon-to-be-successor, Lt. Gen. Ray Odierno, and the No. 2 U.S. commander in Iraq, Lt. Gen. Lloyd Austin, has been doing what he calls "battlefield calculus" - studying ways of adjusting the positioning of U.S. troops in Iraq to possibly enable an overall reduction.
The commander of U.S. forces in western Iraq, for example, has said he could get by with fewer troops because security there has improved markedly and Iraq's army and police have gotten better. Security is more of an issue in areas north and northeast of Baghdad.
Based on that study, results of which have been provided by Petraeus to his superiors in Washington - and weighing a range of other factors such as trends in the level of violence - Petraeus has come up with "tentative recommendations" to Gates and others, the senior military officer said.
"However, the analysis is still ongoing and no decisions have yet been made," the officer said.
Adding to the calculations on troop reductions in Iraq is a growing concern in the U.S. government about a resurgent Taliban insurgency in Afghanistan and unfulfilled demands by U.S. commanders there for more U.S. troops. Significant additions in Afghanistan can't happen without reductions in Iraq.
Col. Peter Mansoor, who served as a close adviser to Petraeus in Baghdad until recently and is retiring from the Army in September, said in a telephone interview Thursday that while he is not involved in Petraeus' new assessment, he sees little reason to think that Petraeus would resist troop cuts.
"It's my belief, given the improvement in the security situation in Iraq, that there will be a continued withdrawal of U.S. forces, as promised by Gen. Petraeus at his last congressional hearing, later this fall," Mansoor said.
The senior military officer who disclosed that Petraeus had made an initial recommendation also told the AP that Afghanistan and other factors, such as war strains on the overall U.S. military, are considered in Petraeus' calculations on troop levels but are not decisive factors.
There is no specific deadline for Petraeus to submit his final recommendation, although it is expected before he turns over the U.S. military command in Baghdad in mid-September to Odierno. Petraeus' next assignment is as commander of U.S. Central Command, where he will be responsible for U.S. military involvement across the Middle East and Central Asia, including Iraq and Afghanistan.
It would be a major surprise if Petraeus did not recommend that troop reductions resume soon. In May, when he testified before the Senate Armed Services Committee, he suggested he was leaning in that direction.
"My sense is that I will be able to make a recommendation at that time for some further reductions," he said, referring to September. He made a point of saying then that the cuts might be modest.
"But I do believe there will be certain assets that, as we are already looking at the picture right now, we'll be able to recommend can be either redeployed or not deployed to the theater in the fall," he said.