The U.S. military believes it has dealt devastating and perhaps irreversible blows to al-Qaeda in Iraq in recent months, leading some generals to advocate a declaration of victory over the group, which the Bush administration has long described as the most lethal U.S. adversary in Iraq.

But as the White House and its military commanders plan the next phase of the war, other officials have cautioned against taking what they see as a premature step that could create strategic and political difficulties for the United States. Such a declaration could fuel criticism that the Iraq conflict has become a civil war in which U.S. combat forces should not be involved. At the same time, the intelligence community, and some in the military itself, worry about underestimating an enemy that has shown great resilience in the past.

"I think it would be premature at this point," a senior intelligence official said of a victory declaration over AQI, as the group is known. Despite recent U.S. gains, he said, AQI retains "the ability for surprise and for catastrophic attacks." Earlier periods of optimism, such as immediately following the June 2006 death of AQI founder Abu Musab al-Zarqawi in a U.S. air raid, not only proved unfounded but were followed by expanded operations by the militant organization.

There is widespread agreement that AQI has suffered major blows over the past three months. Among the indicators cited is a sharp drop in suicide bombings, the group's signature attack, from more than 60 in January to around 30 a month since July. Captures and interrogations of AQI leaders over the summer had what a senior military intelligence official called a "cascade effect," leading to other killings and captures. The flow of foreign fighters through Syria into Iraq has also diminished, although officials are unsure of the reason and are concerned that the broader al-Qaeda network may be diverting new recruits to Afghanistan and elsewhere.

The deployment of more U.S. and Iraqi forces into AQI strongholds in Anbar province and the Baghdad area, as well as the recruitment of Sunni tribal fighters to combat AQI operatives in those locations, has helped to deprive the militants of a secure base of operations, U.S. military officials said. "They are less and less coordinated, more and more fragmented," Lt. Gen. Raymond T. Odierno, the second-ranking U.S. commander in Iraq, said recently. Describing frayed support structures and supply lines, Odierno estimated that the group's capabilities have been "degraded" by 60 to 70 percent since the beginning of the year.

Lt. Gen. Stanley McChrystal, head of the Joint Special Operations Command's operations in Iraq, is the chief promoter of a victory declaration and believes that AQI has been all but eliminated, the military intelligence official said. But Adm. William J. Fallon, the chief of U.S. Central Command, which oversees Iraq and the rest of the Middle East, is urging restraint, the official said. The military intelligence official, like others interviewed for this report, spoke on the condition of anonymity about Iraq assessments and strategy.

Senior U.S. commanders on the ground, including Gen. David H. Petraeus, the head of U.S. forces in Iraq, have long complained that Central Command, along with the CIA, is too negative in its analyses. On this issue, however, Petraeus agrees with Fallon, the military intelligence official said.

For each assessment of progress against AQI, there is a cautionary note that comes from long and often painful experience. Despite the increased killings and captures of AQI members, Odierno said, "it only takes three people" to construct and detonate a suicide car bomb that can "kill thousands." The goal, he said, is to make each attack less effective and lengthen the periods between them.

Right now, said another U.S. official, who declined even to be identified by the agency he works for, the data are "insufficient and difficult to measure."

"AQI is definitely taking some hits," the official said. "There is definite progress, and that is undeniable good news. But what we don't know is how long it will last . . . and whether it's sustainable. . . . They have withstood withering pressure for a long period of time." Three months, he said, is not long enough to consider a trend sustainable.

Views of the extent to which AQI has been vanquished also reflect differences over the extent to which it operates independently from Osama bin Laden's central al-Qaeda organization, based in Pakistan. "Everyone has an opinion about how franchisement of al-Qaeda works," a senior White House official said. "Is it through central control, or is it decentralized?" The answer to that question, the official said, affects "your ability to determine how successfully [AQI] has been defeated or neutralized. Is it 'game over'?"

In Baghdad, the White House official said, the group's "area of operations has been reduced quite a bit for a variety of reasons, some good and some bad." Three years of sectarian fighting have eliminated many mixed Sunni-Shiite neighborhoods. Those areas had been the most fertile and accessible places for AQI, which is composed of extremist Sunnis, to attack Shiite civilians, security forces and government officials. But the death of mixed neighborhoods also has made another Bush administration priority -- promoting political reconciliation -- more difficult.

The expanded presence of U.S. troops in combat outposts in many parts of Baghdad has also put pressure on AQI, but a major test of gains against the organization will come when the U.S. military begins to turn security in those areas over to Iraqi forces next year.

Recent suicide bombings in northern Iraq have convinced some officials that AQI has moved its operations in that direction. But the officials said they do not know whether AQI militants have permanently decamped from Baghdad and Anbar province, or whether they are merely lying low in anticipation of a U.S. departure or the failure of Shiite Prime Minister Nouri al-Maliki to end the sectarian divisions that AQI fostered and now feeds upon.

While a victory declaration might have the "psychological aspect" of discouraging recruitment to a perceived lost cause, the White House official said, advantages overall would be minimal. "I recognize that there are pros to saying, 'Hey, listen, the bad guys are on the run.' " But if AQI were later able to demonstrate residual capabilities with a series of bombings, "even though it was temporary," he said, "the question becomes: How does this play out in terms of public opinion?"