The U.S. military fought its way into downtown Baghdad yesterday and suffered what were by historical standards light casualties for urban combat, with two soldiers and two Marines killed in separate attacks, six others missing and more than 15 wounded.

Those combat deaths were not included in an official Pentagon accounting through Sunday that listed 89 fatalities in the war against Iraq, including 73 Americans killed in action and 16 who died in accidents or other incidents since the conflict began March 19. A total of seven troops are reported missing in action, and seven more are being held by the Iraqis as prisoners of war.

"I predicted there could be anywhere from 100 to 5,000 coalition soldiers killed," said Michael O'Hanlon, a military analyst at the Brookings Institution. "I saw the number 100 as almost as implausible as 5,000. I am very struck that we are at the lower end of what I thought was a wide plausible range."

International health organizations warned yesterday that Baghdad's hospitals have been overwhelmed by casualties now that fierce urban combat has erupted across Iraq's capital, with supplies dwindling and medical personnel caught in the crossfire and unable to report to work.

The World Health Organization in Geneva reported that Baghdad hospitals were seeing 100 combat casualties per hour after a column of U.S. tanks made an initial thrust into the city, and that amputations were apparently being performed without sufficient anesthesia or morphine. WHO spokesman Ian Simpson said doctors and nurses who managed to report for duty at Baghdad hospitals were increasingly finding conditions untenable, with stocks of medicine and supplies -- badly depleted by 12 years of international sanctions -- vanishing in the crush of civilian and military casualties.

As the death toll climbs and human misery increases, so does concern that the U.S. military may be alienating the populace it says it is liberating, and fueling anger in Arab countries and elsewhere.

The WHO also warned yesterday that Iraqi civilian and military casualties will undoubtedly affect the psychological well-being of children, especially in light of the Iraqi military's heavy reliance on conscripts who often are fathers, uncles and brothers who wanted no part of war.

Defense Department officials have been loath to estimate a total number of Iraqi military dead. But one senior Pentagon official estimated that between 2,000 and 4,000 Iraqi soldiers had been killed in Baghdad since Saturday. Many more, the official said, have undoubtedly been wounded.

With the long-awaited urban battle for Baghdad underway, increasing the potential for civilian casualties, there has been no reliable estimate of how many Iraqi civilians may have died in the fighting.

The International Committee of the Red Cross has been touring Iraqi hospitals since the war began. But Amanda Williamson, a Red Cross spokeswoman, cautioned that those visits have been primarily in and around Baghdad and Basra, the nation's two largest cities.

An international antiwar consortium led by Marc Herold, an associate professor of economic development and international affairs at the University of New Hampshire, estimates that between 877 and 1,050 civilians have been killed, based on news reports from Iraq.

But there is no independent confirmation of that number from government sources or major non-governmental organizations. During the war in Afghanistan, Herold's group was criticized for double or even triple counting in casualty reports.

There is little doubt, however, that public health conditions are rapidly deteriorating throughout Iraq, as electric power plants and water pumping facilities are shut down. The World Health Organization reported that 1.5 million people in Basra were without water, and outbreaks of diarrhea have been reported in Basra, Safwan and Nasiriyah.

The WHO's concern about the emotional well-being of Iraqi children stems from the fact that Iraqi military service is compulsory, with about 274,000 men conscripted annually, according to Anthony Cordesman, a defense analyst at the Center for Strategic and International Studies. Many of those conscripts were cannon fodder during the 1991 Persian Gulf War, when an estimated 10,000 to 15,000 Iraqi soldiers were killed, said William Arkin, an independent defense analyst who developed some of the most authoritative casualty estimates of that campaign.

"If your point here is to minimize civilian harm, you can't slaughter military people and think that you've evaded that issue," Arkin said. "They all have families. If we leave thousands or tens of thousands of families without young men, we're going to pay a price in the postwar period."

Simpson, the WHO spokesman, echoed his concern. "It's very easy for the coalition to say we've only hit military targets, but you're still killing people, and people have families. If the aim of your military campaign is to win over the hearts and minds of the people, then killing large numbers of conscripts is not going to help."

A Pentagon official strongly disagreed, saying that thousands of Iraqi soldiers, out of apparent concern for their families and themselves, have surrendered or put down their weapons and faded into the countryside, as U.S. forces have urged. As for U.S. casualties in Baghdad, defense officials and analysts attributed the relatively light number to a combination of U.S. tactics and Iraqi troops' inability to fight effectively or exercise central command and control.

Retired Army Gen. Montgomery C. Meigs, a tank commander in the 1991 Gulf War, said U.S. commanders have been using a tactic he called "reconnaissance in force," probing Iraq's defenses with armored columns supported by air power.

"Commanders are being aggressive but judicious in what they've done," Meigs said. "You take [the city] a bite at a time, which you can definitely dominate and control. And I think that's what's happening. They're not just going to go wailing in there."

Randy Gangle, director of the Center for Emerging Threats and Opportunities at the Marine Corps Warfighting Laboratory, said that a decade of emphasis on urban warfare training is paying dividends, since urban losses historically have run in the range of 30 percent of combatants.

But there is no denying, said Michael Vickers, a former Special Operations officer and CIA operative now at the Center for Strategic and Budgetary Assessments, that Iraq's "bizarre" tactics have helped keep U.S. casualties relatively low.

"They lightly defend things and they lose them," Vickers said. "And then they do headlong counterattacks against them -- and they get slaughtered."

Injured Iraqis are treated at Baghdad's al-Kindi Hospital. The battle for the capital greatly increases the potential for civilian casualties.Marines of the 3rd Battalion, 4th Regiment, escort a comrade in shock after an Amtrac assault vehicle was hit by an Iraqi artillery shell in the fighting for a key bridge into Baghdad.