The partial pullback along the southern and western edges of the city is reported to be part of an apparent security deal discussed with local leaders.
But details of the partial pullback and security deal behind it are vague.
However, U.S. officials in Washington have yet to confirm the deal. The top commander for U.S. forces in Iraq, General John Abizaid, today called the discussions a "possible breakthrough" in efforts to find a peaceful solution to the Al-Fallujah crisis.
Speaking to reporters from Qatar he said, "It's a possible breakthrough, but certainly the conditions that must be met are foremost in our minds."
In his remarks, Abizaid attempted to clarify the tentative deal.
"What we have there is an opportunity, and not necessarily an agreement. The opportunity is to build an Iraqi security force from former elements of the army that will work under the command of coalition forces."
The developments in Al-Fallujah come as U.S. forces today conclude their costliest month ever in Iraq, with more soldiers killed in April than during the invasion last year. The toll for U.S. soldiers for this month is at least 125 killed and, by some reports, close to 1,000 wounded.
The high casualty rate is forcing the U.S. military to review whether soldiers have adequate protection for fighting Iraq insurgents, who appear to have ample stores of roadside mines, rocket-propelled grenades, and improvised explosive devices with which to ambush patrols and convoys.
A top U.S. officer, Marine Corps General John Sattler, told reporters yesterday that the military is rushing more tanks and other heavily armored vehicles to Iraq in response to requests from American field commanders in the so-called Sunni Triangle area.
A U.S. defense official told Reuters privately that "a couple of dozen" Abrams tanks were sent from Germany to the forces in Iraq. He said a number of Bradley Fighting Vehicles -- an armored, tractored personnel carrier -- are also being delivered, but did not specify the amount.
The deliveries come as press reports say U.S. forces were caught by surprise by the intensity of the fighting in April, which followed months of relative calm since the last big upsurge of violence in November.
New U.S. forces rotating into Iraq earlier this year left much of their stocks of heavily armored vehicles in the United States amid expectations that Iraq's security situation was improving.
General Sattler, director of operations for the U.S. Central Command in charge of the Iraqi theater, said this week that U.S. forces are better equipped for peacekeeping than for protection against guerrilla attacks.
He said that "as the security environment was [seen earlier this year as] moving in a very positive direction, the need for tanks and tractored vehicles was overshadowed by the need for wheeled vehicles and warriors on the ground."
The U.S. weekly magazine "Newsweek" reports that, one year ago, the Pentagon had more than 400 main battle tanks in Iraq. It quotes a senior defense official as saying privately that as of recently, there was barely a brigade's worth of tanks in the country. A brigade usually has about 70 tanks. The remainder were rotated out.
The magazine also reports that the U.S. Army's 1st Cavalry Division -- which includes a unit deployed in Baghdad's restive Sadr City neighborhood -- left five of every six of its tanks in the United States and five of every six of its Bradley armored personnel carriers.
Analysts say the U.S. strategy was to begin reducing the use of heavily armored vehicles as part of efforts to focus on counterinsurgency and community-outreach initiatives instead.
Phillip Mitchell, a ground power specialist at the International Institute for Strategic Studies in London, says that those initiatives require soldiers to move about in light vehicles in hopes of winning the confidence of the population.
He says the aim is to induce the public to come forward with information about insurgents -- something they won't do if they are frightened by heavily armored foreign forces moving through their neighborhoods.
"Certainly you cannot take tanks and Bradley Fighting Vehicles within an urban environment; they just don't work," he said. "It's the wrong presentation of the military [occupation] within the various areas where they are patrolling. You want a much lighter approach."
Most of the U.S. soldiers killed in Iraq are reported to have died while in relatively lightly protected vehicles ambushed with roadside bombs or rocket-propelled grenades. The standard light vehicle for patrols is the Humvee.
Some officers have complained that the Humvee does not provide adequate protection. The assistant division commander of the 1st Armored Division, General Mark Hertling, said recently that the Humvee "was never designed to do this...It was never anticipated that we would have things like roadside bombs in the vast number that we've had here."
Military expert Mitchell says that standard Humvees protect only against attacks with assault rifles at mid-range. The vehicles were originally designed for battlefield reconnaissance, where their light armor assures speed and mobility as they scout ahead of advancing forces.
"The Humvees are virtually soft-skinned [unprotected]," he said. "They are armored vehicles but they are only effective against rifles and certainly provide no protection against IEDs [Improvised Explosive Devices] which have been put alongside the roads. The explosions from those sort of devices will tear through the sides of a Humvee, and this is exactly what has been happening."
U.S. soldiers are reported to have tried to fortify their Humvees by bolting on heavy metal plates or strapping on sandbags. The Pentagon is reported to have ordered military outfitters in the United States to increase production of a fortified version of the Humvee for use in Iraq.
The U.S. will now have to decide how to balance the need for better force protection with its continuing desire to move from a combat to a peacekeeping profile in the country. One hope is to increasingly turn over security to Iraqi security forces now being trained by the United States.
Analysts say the shortage of heavily armored vehicles is the main reason for the high casualty rates being sustained by U.S. soldiers, but that there are other factors as well.
One problem is that Iraq's insurgents appear to have formal military training and are proving to be good tacticians. The expertise is apparent in the size of many of the IEDs used to ambush vehicles. The devices can produce huge explosions and require skilled bomb makers to produce.
Many commentators have noted that such attacks would yield a much higher death count if not for recent advances in battlefield medicine. Those advances include techniques for immediately stabilizing the wounded and then rapidly evacuating them to medical centers in Iraq or to U.S. military hospitals in Germany.
U.S. military medical researchers are now studying the patterns of wounds inflicted in Iraq to develop new techniques specifically suited to America's most sustained conflict since the Vietnam War.
Among the research subjects is how to improve personal body armor worn by soldiers to defend them from wounds to upper-body areas like the shoulders, which are now unprotected.