The Ministry of Industry and Information Technology issued a draft plan last April to halt all exports of heavy rare earths, partly on environmental grounds and partly to force other countries to buy manufactured products from China. When the plan was reported on Sept. 1, Western governments and companies strongly objected and Ms. Wang announced on Sept. 3 that China would not halt exports and would revise its overall plan. But the ministry subsequently cut the annual export quota for all rare earths by 12 percent, the fourth steep cut in as many years.

Congress responded to the Chinese moves by ordering the Defense Department to conduct a comprehensive review, by April 1, of the American military’s dependence on imported rare earths for devices like night-vision gear and rangefinders.

Western users of heavy rare earths say that they have no way of figuring out what proportion of the minerals they buy from China comes from responsibly operated mines. Licensed and illegal mines alike sell to itinerant traders. They buy the valuable material with sacks of cash, then sell it to processing centers in and around Guangzhou that separate the rare earths from each other.

Companies that buy these rare earths, including a few in Japan and the West, turn them into refined metal powders.

“I don’t know if part of that feed, internal in China, came from an illegal mine and went in a legal separator,” said David Kennedy, the president of Great Western Technologies in Troy, Mich., which imports Chinese rare earths and turns them into powders that are sold worldwide.

Smuggling is another issue. Mr. Kennedy said that he bought only rare earths covered by Chinese export licenses. But up to half of China’s exports of heavy rare earths leave the country illegally, other industry executives said.

Zhang Peichen, deputy director of the government-backed Baotou Rare Earth Research Institute, said that smugglers mix rare earths with steel and then export the steel composites, making the smuggling hard to detect. The process is eventually reversed, frequently in Japan, and the rare earths are recovered. Chinese customs officials have stepped up their scrutiny of steel exports to try to stop this trick, one trader said.