Neither China’s Ministry of Public Security nor the Ministry of Foreign Affairs responded to faxes requesting comment. But Chinese officials have often boasted about their global efforts to hunt economic fugitives, and the state news media has featured reports detailing the aims and successes of Operation Fox Hunt.

According to the Chinese news media, Beijing has sent scores of security agents abroad to “persuade” their targets to return home. Just how they accomplish their aims is unclear, and questions have been raised about why a number of suspects, presumably sitting on significant wealth abroad, have willingly returned to China.

Liu Dong, a director of Operation Fox Hunt, has said Chinese agents must comply with local laws abroad and that they depend on cooperation with the police in other countries, according to a news report last year. But in a telling admission, he added, “Our principle is thus: Whether or not there is an agreement in place, as long as there is information that there is a criminal suspect, we will chase them over there, we will take our work to them, anywhere.”

It is unclear whether the F.B.I. or the Department of Homeland Security has advocated within the Obama administration to have the Chinese agents expelled from the country, but the White House decision to have the State Department issue a warning to the Chinese government about the activities could be one initial step in the process.

The F.B.I. and the Department of Homeland Security are in charge of tracking the activities of foreign government agents inside the United States, and American officials said that both agencies had amassed evidence about the Chinese law enforcement agents by speaking to Chinese expatriates and by monitoring the agents themselves.

One American official acknowledged that Chinese agents had been trying to track down Ling Wancheng, a wealthy and politically connected businessman who fled to the United States last year and had been living in a lavish home he owns outside Sacramento. Should he seek political asylum, he could become one of the most damaging defectors in the history of the People’s Republic.

Chinese state news media published Interpol alerts in April for 100 people that Beijing described as its most-wanted fugitives worldwide. But experts who have studied the names raised doubts whether the listed men and women are truly the government’s top priority. Among the alleged fugitives, they said, are a former deputy mayor, employees of state-owned enterprises and a history professor, but few if any at the highest echelons of power.