The American warning, which was delivered to Chinese officials in recent weeks and demanded a halt to the activities, reflects escalating anger in Washington about intimidation tactics used by the agents. And it comes at a time of growing tension between Washington and Beijing on a number of issues: from the computer theft of millions of government personnel files that American officials suspect was directed by China, to China's crackdown on civil liberties, to the devaluation of its currency.
Those tensions are expected to complicate the state visit to Washington next month by Xi Jinping, the Chinese president.
The work of the agents is a departure from the routine practice of secret government intelligence gathering that the United States and China have carried out on each other's soil for decades. The Central Intelligence Agency has a cadre of spies in China, just as China has long deployed its own intelligence operatives into the United States to steal political, economic, military and industrial secrets.
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In this case, said American officials, who discussed details of the operation only on the condition of anonymity because of the tense diplomacy surrounding the issue, the Chinese agents are undercover operatives with the Ministry of Public Security, China's law enforcement branch charged with carrying out Operation Fox Hunt.
The campaign, a central element of Mr. Xi's wider battle against corruption, has proved popular with the Chinese public. Since 2014, according to the Ministry of Public Security, more than 930 suspects have been repatriated, including more than 70 who have returned this year voluntarily, the ministry's website reported in June. According to Chinese media accounts, teams of agents have been dispatched around the globe.
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American officials said they had solid evidence that the Chinese agents — who are not in the United States on acknowledged government business, and most likely are entering on tourist or trade visas — use various strong-arm tactics to get fugitives to return. The harassment, which has included threats against family members in China, has intensified recently, officials said.
The officials declined to provide specific evidence of the activities of the agents.
The United States has its own history of sending operatives undercover to other nations — sometimes under orders to kidnap or kill. In the years after the Sept. 11, 2001, attacks, the C.I.A. dispatched teams abroad to snatch Qaeda suspects and spirit them either to secret C.I.A prisons or hand them over to other governments for interrogation.