The explosion offered a rare glimpse into the mostly unseen work of the survey group. Their efforts have been largely unavailing, and Monday's ill-fated search, at a row of stores that provide chemicals for the cosmetics industry, suggested something of the complexities involved.

Brig. Gen. Mark Kimmitt, chief spokesman for the American command, said the tip-off that drew the survey group to raid the store suggested that it was used to produce "chemical munitions" as well as chemical agents used in bomb-making, for insurgent groups. Asked to identify the munitions, he replied, "It could be smoke, it could be anything," meaning smoke bombs. He added: "But it apparently had enough credibility to it, the information, that we sent coalition forces in to do the inspection."

At perfume shops along the street from the explosion, owners sweeping up shards of glass pointed to rows of decanters labelled with the names of scents. Hamad Taha, 39, one proprietor, was incredulous. "The American forces are always coming and searching this area because they think people are providing the raw chemicals for explosives," he said. "We have ethanol, alcohol and acetone for nail polish remover and cosmetics, as well as chemicals for perfume-making. Instead of breaking the door of the store down, the Americans should have asked us to explain it all to them."

When the perfume makers' protests were relayed to Kimmitt, it was his turn to be incredulous. "There was quite an explosion inside that building, which cost the life of two coalition soldiers, injured a number of them and a number of Iraqi civilians," he said. "So if it was making lipstick, that's some pretty high-test lipstick."

At Fallujah, the fighting around the mosque underscored the odds against a lasting breakthrough to avert a military showdown. The agreement on Sunday to have joint American and Iraqi patrols through the city came as a huge relief to many Iraqis, especially in Baghdad, where there were fears that a resumed Marine offensive could set off a tidal wave of anti-American violence that would sweep through Sunni and Shiite neighborhoods alike.

But Monday's events revived the widespread conviction that both sides have made Fallujah a watershed of the wider Iraqi struggle, and that neither the American forces nor the insurgents will back down. If the battle at the mosque suggested that the insurgents were still a long way from submitting, it also showed the Marines' willingness to use some of the heaviest weapons in their arsenal to subdue them.

Kimmitt said the Marines reacted to the first volleys from the mosque, in the northwestern district of Jolan, by advancing under fire, then pausing to allow the insurgents a chance to come out with their hands raised. When nobody emerged, the general said, Marines went in and found the mosque deserted, "with the exception of a significant amount of expended shell casings in the minaret."

He said the Americans pulled back, only to take renewed fire from the mosque. A CNN camera team caught the intensity of the ensuing battle: machine-gunners, crouched with fellow Marines feeding ammunition belts into the breech, firing long bursts from sandbagged positions overlooking the mosque; helmeted troops running from one upper room to another, against a rattle of incoming fire, then hastening down residential streets lined with red bougainvillea blossoms.

Kimmitt said rehearsals were under way for the joint patrols, which would take Marines and their Iraqi companions beyond the Marines' lines of control, with orders to arrest or kill anybody found carrying weapons. But much else in his remarks about Fallujah suggested that the American command sees little likelihood of the insurgents disarming and giving up their fight.