General Petraeus’s advisers say he has stepped back in part because Mr. Obama has handpicked his own public face for the war in Afghanistan, Gen. Stanley A. McChrystal, who last week gave an interview to CBS’s “60 Minutes,” met with Mr. Obama on Air Force One and used a speech in London to reject calls for scaling back the war effort.

Image Gen. David H. Petraeus was the face of the Iraq troop surge. Credit... Stephen Crowley/The New York Times

If anything, General McChrystal’s public comments may prove that General Petraeus might be prudent to take a back seat during the debate. On Sunday, when CNN’s John King asked Gen. James L. Jones, the national security adviser, if it was appropriate for a man in uniform to appear to campaign so openly for more troops, General Jones replied, “Ideally, it’s better for military advice to come up through the chain of command.”

How much General Petraeus’s muted voice will affect Mr. Obama’s decision on the war is unclear, but people close to him say that stifling himself in public could give him greater credibility to influence the debate from within. Others say that his biggest influence may simply be as part of a team of military advisers, including General McChrystal and Adm. Mike Mullen, the chairman of the Joint Chiefs of Staff.

The men are united in what they see as the need to build up the American effort in Afghanistan, although General Petraeus, who works closely with General McChrystal, said last week that he had not yet endorsed General McChrystal’s request for more troops.

Together the three are likely to be aligned against Vice President Joseph R. Biden Jr., as well as other administration officials who want to scale back the effort. In that situation, Defense Secretary Robert M. Gates, who has worried about a big American presence in Afghanistan but left the door open to more troops, could be the most influential vote.

What is clear is that General Petraeus’s relationship with Mr. Obama is nothing like his bond with Mr. Bush, who went mountain biking with the general in Washington last fall, or with Mr. Obama’s opponent in the 2008 presidential campaign, Senator John McCain of Arizona, whose aides briefly floated the general’s name last year as a possible running mate.

By then the general had been talked about as a potential presidential candidate himself, which still worries some political aides at the White House.