The officials, with trade experts, blame America for overstating the potential dangers of certain goods or passing on tips about illicit shipments that are inaccurate or too vague to act.

“They like to exaggerate, or at least try to point to some strategic significance of the item, like saying, ‘This software program could be used to design nuclear power plants,’ even if someone is just buying it to draw puppies and flowers,” said Clif Burns, an export control lawyer at Powell Goldstein in Washington.

American officials have been increasingly alarmed about trade in the United Arab Emirates since 2002, when the Commerce Department sent an inspector, Mary O’Brien, there. From her spot checks of factories, freight forwarders and other companies that had ordered American products subject to export controls, Commerce officials say, it was clear that dual-use goods, including computer equipment, were being diverted on a grander scale than imagined.

An entity said to be a woodworking shop, for example, had ordered a sophisticated American machine for making metal parts. The device, Ms. O’Brien knew, could also shape components for a missile system. The supposed factory contained almost no sawdust, and the few employees could not explain how they intended to use the machine.

“This is not right,” Ms. O’Brien said she had said to herself, convinced that she had turned up her first “briefcase business” open for inspection, but closed for good as soon as she walked out.

She pressed a Dubai pistachio wholesaler on why he had bought an American infrared camera, which can detect living objects in the dark, and where it had gone. Later she found he had arranged its return from Iran, where it had apparently been diverted, while stalling a follow-up inspection.

In nearly 40 percent of her inspections in four years, she found that regulated items were missing or that the recipient would not cooperate. Many of those companies were placed on a list, warning American exporters to be careful when selling to them.