By EDMUND L. ANDREWS

AMAWA, Iraq, May 26 — Iraqi officials here say that they asked American military leaders as early as a month ago to help protect major archaeological sites from looters, but that for the most part, their pleas were ignored and artwork and relics from ancient Babylon are still being stolen from many locations.

Marine officials said they had taken care to protect Babylon and a handful of other famous ruins from looters. But they also made it clear in the last few days that protecting archaeological treasures was merely one of many priorities, and not necessarily the top one.

On a visit Sunday, three sites near here were pocked with freshly dug holes and littered with hastily abandoned shovels, indicating looting in the last day or two. At one spot, about two dozen people ran off when they saw approaching trucks.

At Isan Bakhriat, site of the ancient city of Isin to the north of here, more than 100 looters were openly digging out and selling urns, sculptures and cuneiform tablets.

"It's happening at almost every site," said Tofiq Abed Muhammad, director of antiquities for the province of Samawa. "They are smart. They take the antiquities that they know have value, and they know how to get them out of the country."

The plundering of Iraqi archaeological sites is the second major wave of culture theft since American forces toppled the government of Saddam Hussein in early April.

The first wave came as American soldiers were seizing Baghdad, when looters broke into and largely gutted Iraq's national museums.

The archaeological lootings could amount to even larger losses over time. Archaeologists say the sites have been so disrupted that systematic historical research there may now be impossible.

Mr. Muhammad said his first request for help was to Lt. Col. Daniel O'Donahue, the commanding officer at a Marine base just outside Samawa.

"We told them we needed American soldiers at checkpoints, in combination with Iraqi guards," he said.

Colonel O'Donohue confirmed that he had discussed the issue. But he said marines were attending to more basic needs like securing enough water, food and medical care for people in the area.

"We don't have anywhere near enough marines to police every fixed site in the country," he said. "Our view is that if it's a fixed site, it's primarily an Iraqi responsibility."

The First Marine Division has primary responsibility for overseeing southern Iraq, which is where cities like Babylon, Isin and the Sumerian Uruk were all situated.

Marine officials said they had taken care to protect Babylon and a handful of prized ancient ruins from looters and other forms of attack. But they also made it clear that protecting antiquities was merely one of many tasks before them.

"It comes down to what the priorities are," said Lt. Col. Richard S. Long, a spokesman for the First Marine Division. "You have to put the securing of those archaeological sites within the mosaic of ensuring food, water, electricity, sewage and other types of basic needs."

Looters were discovered at work on Thursday at the ruins of Isin, which was a powerful city around 1900 B.C. and again around 1100 B.C.

On Sunday afternoon, the First Marine Division sent a patrol unit to investigate. The troops saw evidence of looting at the site, but no looters. But today, residents of the nearby town of Afak said the diggers had resumed activity at close to their normal pace.

Here in Samawa, Iraqi officials said they felt powerless to stop the looters. The police force here, like others across the country, disintegrated when American forces crushed Mr. Hussein's government.

"Two weeks ago, I went to talk to American officials who were collecting weapons as part of an effort to disarm people," recounted Jacob Youssef Hussein, a guard at one of many archaeological sites in the nearby desert. "I asked him to help us secure these sites. He said that was our problem, not his problem."

Colonel O'Donahue said the marines were ready to arm, train and even pay Iraqis to guard the sites.

But Iraqis involved with the archaeological sites say they have heard no such offer. One of their biggest worries is a new edict by the American civilian administrator, L. Paul Bremer III, that prohibits most Iraqis from carrying guns outside their homes.

Iraqis fear that the edict will prohibit the Bedouin watchmen who have long guarded the sites from carrying their beloved Kalashnikovs.

"The Americans must understand that these guards have to carry weapons," Khalid Azara, deputy mayor of Samara, said as he waved a letter he had just written begging the American authorities for gun permits for 35 people.

But arming the existing guards may not be the full solution. Experts and local Iraqis say many guards had themselves become collaborators and even organizers of the looters.

The problem reflects the broader absence of law, and law enforcement, that gave rise to looting of all types. Iraq has virtually no courts and only a fledgling police force, which means that power often resides with those who control the most weapons.

The marines, meanwhile, are tackling dozens of other projects.

"I'm not saying we're stretched too thin," Colonel Long said. But, he added, "Iraq is a big country, and there are a lot of needs."

"As we get information about sites where looting is occurring, we are sending out patrols to investigate the sites — as possible," he said. "I emphasize the words `as possible.' "