WASHINGTON » When President Barack Obama descended into the White House Situation Room on Monday for his monthly update on Afghanistan and Pakistan, the new top U.S. military commander, Gen. David H. Petraeus, ticked off signs of progress.

Come December, when the president intends to assess his Afghan strategy, he will be able to claim tangible successes, Petraeus predicted by secure video hookup from Kabul, Afghanistan, according to administration officials.

The general said that the U.S. military would have substantially enlarged the "oil spot" — military jargon for secure area — around Kabul. It would have expanded U.S. control farther outside of Kandahar, the Taliban heartland. And, the aides recalled, the general said the military would have reintegrated a significant number of former Taliban fighters in the south.

"He essentially promised the president very bankable results," one administration official said. (Others in the room characterized the commander’s list more as objectives than promises.)

Obama largely listened, asking a few questions, and two hours later, the White House sent an e-mail to reporters using language that echoed the general’s.

But even inside an administration that is pinning its hopes, both military and political, on the accuracy of the general’s report, there are doubters. Assessments from intelligence officials are far more pessimistic, and Obama regularly reviews maps that show how the Taliban have spread into areas where they had no major presence before.

And some military officers, who support Petraeus’ counterinsurgency strategy and say he readily acknowledges the difficulties ahead, caution that the security and governance crisis in Afghanistan remains so volatile that any successes may not be sustainable.

How that tension plays out in coming months — the guarded optimism of a popular general leading an increasingly unpopular war and the caution of a White House that prides itself on a realism that it says President George W. Bush and his staff lacked — will probably define the relationship between Obama and his field commander. Petraeus, who led the Iraq surge and was a favorite of Bush’s, has slowly worked himself into the good graces of a president who was once wary of him.

So far, the two men appear to be meshing well, advisers say. They "are actually somewhat similar in temperament and style," said Benjamin Rhodes, the National Security Council’s director of strategic communications. Both are meticulous, even-keeled and matter of fact, and both like to do their homework, studying detailed reports.

Since Petraeus took on the commander’s job in June, several aides said, the president had struck a more deferential tone toward him than he used with Gen. Stanley A. McChrystal, Petraeus’ predecessor. Often during pauses in meetings, one White House official said, Obama would stop and say, "Dave, what do you think?"

Like no other figure today, Petraeus has stepped into Gen. Colin L. Powell’s shoes as the face of the military to ordinary Americans, particularly as the White House extols the end of the combat mission in Iraq, which was largely made possible by the troop surge that Petraeus orchestrated.

For Obama, that may be a blessing and a curse. Petraeus has made clear that he opposes a rapid pullout of troops from Afghanistan beginning in July, as many of the president’s Democratic allies would like. Some in the White House, with an eye on the 2012 presidential election, fear that the general may already be laying the groundwork for keeping a large force in Afghanistan for a long while.

Defense Secretary Robert M. Gates said Thursday that the unresolved question was whether the "campaign plan" for Afghanistan was working.

"The evidence that General Petraeus is seeing so far suggests to him that it is, and both on the civilian and the military side, not just the military side," Gates told reporters. "But he is cautious, and I will be cautious."

The new alliance between Obama and Petraeus holds risks for the general as well as the president. In taking on Afghanistan, he is risking his reputation as perhaps the greatest general of his generation on a war that many people think will end in a stalemate. Even if Petraeus’ strategy is a solid one, few believe Obama will commit the time and resources — many years and hundreds of billions of dollars — needed to test the Petraeus thesis.

Petraeus has a history of early optimistic assessments that proved largely correct; one dates back to the Iraq surge, over which he and Obama first butted heads. Military officials say that during the early days of the surge, Petraeus cited what his staff termed "leading indicators" of progress, even when much of the private and public discussion of the war effort was still negative. (During one Senate hearing with Petraeus, then-Sen. Obama accused the Bush administration of setting "the bar so low that modest improvement in what was a completely chaotic situation" was considered success.)

While Petraeus’ track record in Iraq may give added weight to his analysis on Afghanistan, the two wars are radically different in Obama’s mind, his aides said. During meetings at the White House, the general "always brings up Iraq," one senior administration official said.

While Obama asked Petraeus last fall to assemble the lessons learned in the Iraq surge that could be applied in Afghanistan, the president, by and large, "remains focused on Afghanistan," the official said.

Some officials would speak only on background about interactions they had witnessed in confidential meetings.

In preparation for this fall’s review of the strategy in Afghanistan, Obama’s first request of Petraeus was for new and better ways to measure success or setbacks; the general presented them Monday.

He started with familiar measures: How many Afghan troops have been trained and how many operations have focused on Taliban strongholds in places like Kandahar and Helmand.

Then Petraeus added three others: one looking at local security initiatives enacted by the Afghan police, another at the pace of "reintegration" of former members of the Taliban and a third looking at the successes of attacks by U.S. Special Operations forces.

"These are more specific," said one adviser to the president. "With McChrystal, it was ‘You’ll know victory when you see it.’ The president has asked for a lot more visibility into what’s happening."

Obama gets a wider view from intelligence reports, chiefly from the CIA and the Defense Intelligence Agency, that land on his desk weekly. They assess whether Hamid Karzai’s government in Afghanistan is preparing to survive on its own, or whether the Taliban can successfully retreat to their haven in Pakistan to prepare new attacks. Those longer-range assessments have been significantly more pessimistic than Petraeus’ measures of battlefield progress.

Some national security experts say that the fate of McChrystal — now on the lecture circuit making $60,000 a speech — and the fired general before him, Gen. David D. McKiernan, means Obama must make things work with Petraeus, lest he appear unable to get along with his commanders.

"If they have a falling out, it’s not at all clear that the public would necessarily side with the president the way they did in the McChrystal incident," said David Rothkopf, a former Clinton administration official.

Added Leslie H. Gelb, president emeritus of the Council on Foreign Relations: "They are joined at the hip, but the leverage lies with Petraeus. And Petraeus has made plain, publicly, that after July 2011, he doesn’t think there should be a rapid pullout."