Instead, officers say, the only way to end the guerrilla war is through Iraqi politics - an arena that so far has been crippled by divisions between Shiite Muslims, whose coalition dominated the January elections, and Sunni Muslims, who are a minority in Iraq but form the base of support for the insurgency.
''The more accurate way to approach this right now is to concede that this insurgency is not going to be settled, the terrorists and the terrorism in Iraq is not going to be settled, through military options or military operations,'' Brig. Gen. Donald Alston, the chief U.S. military spokesman in Iraq, said last week, in a comment that echoes what other senior officers say. ''It's going to be settled in the political process.''
Gen. George Casey, the top U.S. commander in Iraq, expressed similar sentiments, calling the military's efforts ''the Pillsbury Doughboy idea'' - pressing the insurgency in one area only causes it to rise elsewhere.
''Like in Baghdad,'' Casey said in an interview last week. ''We push in Baghdad - they're down to about less than a car bomb a day in Baghdad over the last week - but in north-center [Iraq] they've gone up. The political process will be the decisive element.''
The recognition that a military solution is not in the offing has led U.S. and Iraqi officials to signal they are willing to negotiate with insurgent groups, or their intermediaries.
''It has evolved in the course of normal business,'' said a senior U.S. diplomatic official in Baghdad, who spoke on condition of anonymity because of U.S. policy to defer to the Iraqi government on Iraqi political matters. ''We have now encountered people who at least claim to have some form of a relationship with the insurgency.''
The message is markedly different from previous statements by U.S. officials who spoke of quashing the insurgency by rounding up or killing ''dead enders'' loyal to former dictator Saddam Hussein. As recently as two weeks ago, in a Memorial Day interview on CNN's ''Larry King Live,'' Vice President Dick Cheney said the insurgency was in its ''last throes.''
But the violence has continued unabated, even though 44 of the 55 Iraqis portrayed in the military's famous ''deck of cards'' have been killed or captured, including Saddam.
Lt. Col. Frederick Wellman, who works with the task force overseeing the training of Iraqi security troops, said the insurgency is not running out of new recruits, a dynamic fueled by tribal members seeking revenge for relatives killed in fighting.
''We can't kill them all,'' Wellman said. ''When I kill one I create three.''
Last month was one of the deadliest since President Bush declared the end of major combat operations in May 2003, a month that saw six American troops killed by hostile fire. In May 2005, 67 U.S. soldiers and Marines were killed by hostile fire, the fourth-highest tally since the war began, according to Iraq Coalition Casualty Count, an Internet site that uses official casualty reports to organize deaths by a variety of criteria.
At least 26 troops have been killed by insurgents so far in June, bringing to 1,311 the number of U.S. soldiers killed by hostile action. An additional 391 service members have died as a result of accidents or illness.
The Iraqi interior minister said last week that the insurgency has killed 12,000 Iraqis during the past two years. He did not say how he arrived at the figure.
Events in Iraq
* Four American soldiers are killed, pushing the U.S. death toll in Iraq past 1,700.
* Dozens of Iraqis are found shot to death.
* A French journalist is freed after five months in captivity.