"They come across the border and use Tall Afar as a base to launch attacks across northern Iraq," Col. H.R. McMaster, commander of the Army's 3rd Armored Cavalry Regiment, which led the assault, said in a briefing the day before it began.

When the air and ground operation wound down in mid-September, nearly 200 insurgents had been killed and close to 1,000 detained, the military said at the time. But interrogations and other analyses carried out in recent weeks showed that none of those captured was from outside Iraq. According to McMaster's staff, the 3rd Armored Cavalry last detained a foreign fighter in June.

In a recent interview, McMaster maintained that, before insurgents were driven from Tall Afar in September, foreigners were at least partly responsible for the "climate of fear" that pervaded the city -- a result of beheadings, suicide attacks and the abduction of young men to conscript them as fighters.

"They trained indigenous terror cells and moved on somewhere else," he said.

The relative importance of the foreign component of Iraq's two-year-old insurgency, estimated at between 4 and 10 percent of all guerrillas, has been a matter of growing debate in military and intelligence circles, U.S. and Iraqi officials and American commanders said. Top U.S. military officials here have long emphasized the influence of groups such as al Qaeda in Iraq, an insurgent network led by a Jordanian, Abu Musab Zarqawi. But analysts say the focus on foreign elements is also an attempt to undermine the legitimacy of the insurgency in the eyes of Iraqis, by portraying it as terrorism foisted on the country by outsiders.

"Both Iraqis and coalition people often exaggerate the role of foreign infiltrators and downplay the role of Iraqi resentment in the insurgency," said Anthony H. Cordesman, a former Pentagon official now at the Center for Strategic and International Studies in Washington, who is writing a book about the Iraqi insurgency.

"It makes the government's counterinsurgency efforts seem more legitimate, and it links what's going on in Iraq to the war on terrorism," he continued. "When people go out into battle, they often characterize enemies in the most negative way possible. Obviously there are all kinds of interacting political prejudices they can bring out by blaming outsiders."

In weekly briefings for reporters in Baghdad, Maj. Gen Rick Lynch regularly displays slides showing the face of Zarqawi, whose organization has asserted responsibility for many high-profile attacks. Mug shots of the Jordanian adorn virtually every barracks and checkpoint in Baghdad's fortified Green Zone.

"We do believe that the major players are in Zarqawi's network, and that's why we're focusing our operations against him," Lynch said in a recent interview. "We believe that the most lethal piece of the insurgency here is the terrorist and foreign fighters. And it's because of the level of violence they're willing to go to to accomplish their objective, which is to derail the democratic process and discredit the Iraqi government."

U.S. and Iraqi officials have long maintained that a key to stabilizing the country is preventing an alliance between foreign fighters and Iraqis who might be amenable to pursuing politics instead of violence to accomplish their goals. But as the country's nascent political process has moved forward -- a transitional government has been elected and a constitutional referendum held so far this year, and parliamentary elections are scheduled for next month -- there is little evidence that the native insurgency has diminished.

In much of the country, including the north and center, commanders say, the insurgency is led and populated almost entirely by Iraqis, many of them former members of Saddam Hussein's Baath Party, who do not work closely with Zarqawi's group. Commanders there say Iraqi insurgents are largely responsible for the roadside bombings, some involving armor-penetrating weapons, that have been responsible for roughly half of the U.S. combat deaths in recent months.

"The foreign fighters' attacks tend to be more spectacular, but local nationals, the Saddamists, the Iraqi rejectionists, are much more problematic," said Maj. Gen. Joseph J. Taluto, commander of the Army's 42nd Infantry Division. His unit, which lost 59 soldiers during its tour here, was based in the northern city of Tikrit, Hussein's home town, before transferring the region to the 101st Airborne Division this month.

Al Qaeda in Iraq maintains a presence in the region, he said, "but they're not having much of an impact. Their message is not resonating."

In Washington, a senior State Department official called foreign fighters "an important element to the insurgency," but added that "it would be a mistake to imagine that this isn't a largely Iraqi-based operation with critical support from foreign elements."

A Western diplomat in Baghdad, who spoke on the condition that he not be named, said that foreign fighters remained the coalition's "greatest concern" and that publicizing their role helps the Iraqi government pressure nations whose citizens are traveling to Iraq to fight. "It may be overstated by some, but that does not mean they don't exist," he said. "It is critical to get the help from countries where these people come from, to stop the flow."

Cordesman said the relative influence of foreign and Iraqi elements of the insurgency is difficult to measure because accurate numbers are hard to come by. In a report published in September, he and a co-author said they believed that 4 to 10 percent of the roughly 30,000 insurgents in Iraq are foreigners, many of them adherents of a radical branch of Islam known as Salafism.

They said that interviews with intelligence officials and earlier studies suggested that the largest contingents are Algerians (20 percent), Syrians (18 percent), Yemenis (17 percent), Sudanese (15 percent) and Egyptians (13 percent). They can be hard to distinguish from the general population, the report said, because cell leaders have encouraged them to shave their beards, which symbolize piety, and to carry cigarettes, even though most Salafis do not smoke.

Last month, Lynch said at a news conference that 376 foreigners had been detained in Iraq this year, including 78 Egyptians, 66 Syrians, 41 Sudanese and 32 Saudis. One American and one Briton also were captured, Lynch said.

In Tall Afar, the United States launched a major offensive more than a year ago, but insurgents regained control of much of the city after the Americans reduced troop strength in the region to one battalion.

This September's offensive restored order and has allowed thousands of residents who had fled to return. The vast majority are Sunni Muslim Turkmens, many of whom served in the army under Hussein. Attacks have continued, including a suicide bombing carried out by a mentally disabled Iraqi girl, though less frequently than before, the military reported.

"The enemy in Tall Afar consists mostly of local fighters, with a small but dangerous network of Takfirist foreign leaders, financiers and propagandists," said Lt. Col. Paul Yingling of the 3rd Armored Cavalry, referring to adherents of another radical branch of Islam. Once the regiment arrived "and began to operate with the Iraqi army in the city, the foreign component of the insurgency became much more cautious," he said.

Correspondent John Ward Anderson in Baghdad and staff writer Robin Wright in Washington contributed to this report.