Three men were convicted in Brooklyn federal court on Tuesday of stalking a family in the New Jersey suburbs on behalf of the Chinese government.

The defendants, Michael McMahon, 55, Zhu Yong, 66, and Zheng Congying, 27, were found guilty of stalking and a related conspiracy charge. Mr. Zhu and Mr. McMahon were also found guilty of acting as unregistered foreign agents, and Mr. Zhu was convicted on a second conspiracy charge.

Speaking outside the courthouse on Tuesday, Mr. McMahon, a retired New York Police Department sergeant turned private investigator, maintained his innocence and vowed to appeal.

“If I had known that they were part of a foreign government looking to harass anybody, I would have said no, and I would have called the F.B.I.,” he said.

The verdict capped a three-week trial during which prosecutors laid out a detailed case accusing the men of playing roles in Operation Fox Hunt, a decade-long effort that Chinese officials have said is aimed at repatriating fugitives. The Justice Department contends that the campaign is part of the Communist Party’s push to control Chinese nationals around the world.

The Brooklyn case was the first the Justice Department prosecuted to counter the Chinese operation, and it unfolded as tensions between the rival superpowers reached new heights, with disagreements over China’s growing military footprint and other issues. Secretary of State Antony J. Blinken met with Xi Jinping, China’s leader, in Beijing over the weekend.

The Justice Department has made cases related to China a primary focus in recent years, and the office of the U.S. attorney in Brooklyn, Breon S. Peace, is especially attuned to what it calls “transnational repression” by foreign governments. In a statement after the verdict, Mr. Peace said that Mr. McMahon and Mr. Zhu had acted “at the direction of a hostile foreign state.”

“We will remain steadfast in exposing and undermining efforts by the Chinese government to reach across our border and perpetrate transnational repression schemes targeting victims in the United States in violation of our laws,” he said.

Wang Wenbin, a spokesman for the Chinese Ministry of Foreign Affairs, accused the Justice Department on Friday of “slanders and smears” related to the case, adding that transnational repression “is an allegation that best matches the U.S.’s own practices.”

Mr. McMahon, of Mahwah, N.J., could face up to 20 years in prison, according to the U.S. attorney’s office. But Lawrence Lustberg, his lawyer, said outside the courtroom last week that federal sentencing formulas are complicated, and that he believed the maximum, in practice, would be less than three years. According to prosecutors, Mr. Zhu, of Queens, could face 25 years, and Mr. Zheng, of Brooklyn, could face 10.

Mr. McMahon said outside court that he had notified the local police while conducting surveillance on five separate occasions, and that he had hired other former N.Y.P.D. detectives to help him. Mr. Lustberg had argued at trial that those facts were proof that Mr. McMahon was unaware that the case was connected to the Chinese government.

Renee Wong, a lawyer for Mr. Zheng, said that she considered the verdict good news since he was acquitted of the two top charges, and that her team was considering an appeal of the stalking charge.

“There were no connections between the people that Mr. Zheng knew and the people that Mr. McMahon and Mr. Zhu knew. The connection was simply lacking,” she said.

Kevin Tung, a lawyer for Mr. Zhu, did not immediately return a request for comment.

During the trial, Judge Pamela K. Chen warned everyone involved to focus on the specific allegations, not the international politics swirling around them. The jury began to deliberate on Thursday.

The case centered on Xu Jin, a former Chinese government official who moved to the United States over a decade ago. Prosecutors said the three defendants were key to a plot engineered by Chinese government officials to stalk and harass Mr. Xu and his family and to force him to return to China, where he could have faced the death penalty on an embezzlement charge.

The jury was shown voluminous records documenting communications starting in fall 2016, when Mr. Zhu contacted Mr. McMahon, who was working as a private investigator in New Jersey.

The older man, who did not speak much English, enlisted a translation company in Flushing, Queens, to help him communicate. Mr. McMahon’s understanding was that he was working for a private company seeking to recoup money, Lawrence Lustberg, a lawyer representing him, said.

Mr. McMahon carried out surveillance for five days spread over six months in 2016 and 2017, and unearthed records related to Mr. Xu’s whereabouts and assets. He also met Mr. Zhu’s associate Hu Ji, who turned out to be a police officer in the Public Security Bureau in Wuhan, China.

A face-to-face encounter among the men, at a Panera Bread restaurant in New Jersey, in October 2016, was captured in a photo shown to the jury as evidence of their direct ties.

In the picture, Mr. McMahon is grinning and standing between the two others with his arm around Mr. Zhu. After the meeting, Mr. Hu, using the name Eric Yan, began contacting Mr. McMahon directly with instructions.

Mr. Lustberg argued during the trial that there was no evidence showing that Mr. McMahon knew that his investigation was being directed by the Chinese government. Rather, the emails about it had referred to a “company” requesting the work.

The target of his investigation, Mr. Xu, was once the head of Wuhan’s Municipal Development and Reform Commission, according to reports in Chinese state media. Those reports said he was wanted for embezzlement, abuse of power and accepting bribes. Mr. Xu testified at the Brooklyn trial but could not immediately be reached for comment after the verdict.

The days for which Mr. McMahon was hired coincided with a 2017 trip to New Jersey by Mr. Xu’s ailing 82-year-old father that prosecutors said Chinese officials had forced him to make.

The elder Mr. Xu’s daughter had already been jailed because of his son’s refusal to return home, jurors were told. Chinese officials then plotted to send the elder Mr. Xu to New Jersey to persuade his son to come back to China, prosecutors said. The officials did not know the younger Mr. Xu’s address, and used his father as bait to lure him out and follow him, prosecutors said.

Mr. Xu’s sister-in-law testified about her shock when the older man showed up on her doorstep in Short Hills, N.J., with no warning. She had already received several threats related to Mr. Xu and knew that the Chinese government was trying to find him, she said. To thwart them, she arranged a meeting the next day at a nearby mall, rather than at Mr. Xu’s home.

But the next year, two men, including Mr. Zheng, showed up at his home in Warren, N.J., and left a threatening note. Mr. Zheng’s lawyer, Paul Goldberger, said that his client was “just a kid” who had driven to the home as a favor to the other man, and that he had immediately regretted his actions.

Mr. Zheng even drove back to try and take the note down, Mr. Goldberger said. But he was too late: Mr. Xu testified that he had already done so, following instructions from the F.B.I.