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“They are looking for goods at a certain cost level and this could, annoyingly, lead to products that are counterfeit,” Mr. Drengenberg said of the stores.

They can be an important outlet not only for fakes but also for other dangerous goods, federal officials said.

The Consumer Product Safety Commission (CPSC), for example, has announced well more than a dozen recalls of children”s jewelry this year because they contain lead, which is toxic if ingested. The Chinese-made jewelry is predominantly sold through discount outlets, CPSC spokesman Scott Wolfson said.

A message left with the Retail Dollar Store Association seeking comment was not immediately returned.

Overall, federal regulators are stepping up their scrutiny of Chinese-made goods. Mr. Wolfson said products made in China account for more than 60 percent of the recalls that the CSPC has announced so far this year.