BAGHDAD, Iraq — Some American officers call him "Z." In the military's classified signal traffic, he is "AMZ." By any name, American forces in Iraq have found in Abu Musab al-Zarqawi a mesmerizing target.
If they could capture this Jordanian-born militant, anointed by Osama bin Laden as Al Qaeda's chief in Iraq, American commanders are hoping, they could strike a compelling, perhaps decisive, blow against one crucial component of the Iraqi insurgency - the Islamic militant groups that draw zealots from across the Arab Middle East to carry out suicide bombings, beheadings and other atrocities.
The capture of Saddam Hussein in 2003 dealt the insurrection no such mortal blow, and American commanders know Mr. Zarqawi's capture or death might not either. "It's not about one guy," a senior officer said Friday. "It's more about the network of cells he has across the country. That's where we're applying the pressure."
Still, American officers acknowledge privately, eliminating Mr. Zarqawi would boost American troops' morale like nothing else, and perhaps decapitate the Islamic terrorists whose suicide bombs were a main weapon of the insurgency in the last month. Rebels killed nearly 800 civilians and more than 70 American soldiers during that period, making it one of the war's deadliest months.
That is the backdrop to one of the most important - and, so far, undecided - campaigns of the Iraqi conflict: the American drive to close off insurgent infiltration routes that run into the Iraqi heartland down the Euphrates River corridor. From Husayba on the Syrian frontier through Qaim and the sand-blown towns of Rawa, Haditha, Asad and Hit, onward through Ramadi and Falluja to Baghdad, the corridor has become the Ho Chi Minh trail of this war.
Like the bane of American commanders in Vietnam, the 300-mile stretch of river is not so much a single route as a multi-stranded network of passages, some hewing close to the lush silted landscape of palms and reeds that run along the banks, others crossing vast reaches of stony desert on either side.
Twice since early May, in a constellation of small towns near Qaim and later in a more concentrated sweep around Haditha, the Second Marine Division, backed by American Army units - and at Haditha by Iraqi soldiers - have set out to stifle the Zarqawi network.
But the results have been disappointing, falling far short of stunting the militants' operations.
For the Qaim operation, the marines acted on a tip that Mr. Zarqawi and some of his top lieutenants had found refuge among tribal leaders downriver, in the vicinity of Haditha.
The Americans assembled a 1,000-man battle group that sought to cut off the retreat upriver with a dash across the desert on the river's southern side. Then, close to the Syrian border, the marines crossed to the northern bank on a pontoon bridge. But this was a time-consuming maneuver that cost the crucial element of surprise, some officers said.
Then the Americans ran into fierce resistance at Ubaydi, where repeated Marine assaults, supported by tank fire and 500-pound bombs from an F/A-18 Hornet fighter-bomber, were needed to quell one group of Islamic fighters.
An account by an embedded reporter for The Washington Post described rebels lying on their backs in a crawl space beneath the concrete floor of a house, blasting marines above them with bullets designed to penetrate tanks. When the battle subsided, the marines found that many rebels who were quartered in neighboring towns had fled, some westward into Syria, others eastward into the interior of Iraq.
After the weeklong offensive at Qaim, the Marines estimated they had killed 125 insurgents, while losing nine marines. When the Haditha operation, which involved 1,000 American and Iraqi troops, ended last weekend, the American command was elusive, saying only that "a significant number of terrorists were killed."
In Baghdad, American officers acknowledged that the hope of smashing the infiltration network had been unfulfilled. "I don't know how many scooted," a senior officer said, speaking of the rebels who escaped the cordon at Qaim. Of the infiltration route as a whole, he added, "We still have a problem with people coming across the border."
From the insurgency's first stages, a common complaint among American officers in the field has been that American troops are overstretched, and there were whispers of this, again, after the Marine operations at Qaim and Haditha.
A Marine spokesman at Camp Falluja, Lt. Col. David A. Lapan, responding to questions sent by e-mail, acknowledged that troop levels in Iraq's immense Anbar Province were lower than they were last year. But he said the shortfall was being filled by Iraqi troops. "There are sufficient numbers of forces to accomplish the mission," he said. "The enemy is losing and he knows it."
But a glance at the map, and even a cursory sense of the region's history, suggests the scope of the problem the Americans face. Anbar is the vast western region that encompasses more than a quarter of Iraq, including the Euphrates corridor and nearly 600 miles of border with Saudi Arabia, Jordan and Syria. It has one of the lowest population densities of any of Iraq's 18 provinces, with barely 1.3 million people, many of them living in the cities and towns along the Euphrates. The deserts, of course, are mostly empty; even in the mid-19th century the Bedouins who roamed them were only a tiny fraction of the population, which was recorded as 500,000 in an Ottoman census.
Since that census, camel trains have yielded to Land Cruisers and Pajeros, and the old trading routes to smuggling. American intelligence officers say that trails across the desert used for decades to smuggle herds of sheep and goats, leather hides, car parts, gasoline and sundry other commodities have now been adapted to the insurgents' needs.
The American forces use sophisticated surveillance aircraft and unmanned drones to keep watch, especially along the 310 miles of the frontier with Syria. But how easy it is to slip unnoticed across the desert is something the Americans themselves demonstrated during the last months of Saddam Hussein's dictatorship, when United States forces based in remote areas of eastern Jordan ran deep-penetration missions, some of them all the way to Baghdad.
For their part, the insurgents have access to a resource network of their own - Sunni Arab mosques sympathetic to the insurgency in almost every village and town from Damascus to Baghdad. American officers say they have become stations on a relay run straight into the heart of Iraq.
In numbers, the foreign Arab recruits account for a fraction of the insurgents operating across Iraq, whose total is estimated by the American command to range from 12,000 to 20,000. How small a fraction can be guessed from the fact that, as of last week, only 370 of the 14,000 men held as suspected insurgents in American-run detention centers in Iraq were foreigners, according to figures provided by the American command.
But the significance of the infiltration was starkly evident last week in an incident near Rawa in which the kidnapped governor of Anbar was killed during a shootout between insurgents and an American patrol. The American officer commanding the patrol said the four insurgents who died and three who were captured were all non-Iraqis, from Algeria, Jordan, Morocco, Saudi Arabia and Syria.
Nor is there much doubt that the foreign Arabs' impact has been out of proportion to their numbers, primarily because of the willingness of the non-Iraqis to die in suicide bombings. According to a tally kept by the American command, more than 60 of these bombings took place across the country in May, responsible for about two-thirds of the civilians who died.
Iraqis commonly insist that suicide bombing is alien to the Iraqi character, and American commanders agree. "In every case we've seen, the driver has been a foreigner," an American officer who has studied the bombings said last week.
The officer said intelligence reports had established that many bombers passed through mosques in Damascus, Syria's capital, or Aleppo, another Syrian city, and from there through a network of mosques that filtered, in many cases, down the Euphrates, through Qaim, Haditha and Ramadi. At every stage, the officer said, the handlers were organized in cells, each separate from the next, so as to guard the network's secrecy.
As for the bombers, he said their sojourns in Iraq were generally short.
"They don't stay in Iraq very long," the officer said. "They get a lot of indoctrination along the way, but once they're here they are moved into operations very, very fast."