A Chinese Foreign Ministry spokesman, Zhao Lijian, criticized Washington’s effort, saying it was “doing all it can to pressure other countries to give up their support for the Chinese candidate.” China’s ambassador in Geneva, Chen Xu, told reporters last week that the United States had threatened smaller countries with loss of World Bank and International Monetary Fund loans.

Ms. Wang, who holds a law degree from the University of California at Berkeley and a law diploma from Columbia Law School, was the most qualified candidate, he said, citing her nearly 30 years of service at the United Nations intellectual property office where she is a deputy to the departing director, Francis Gurry of Australia. America’s opposition to her candidacy was “totally irrational,” he added.

But campaigning for the United Nations post touched a nerve in the White House. The Trump administration has accused China of outright theft of American technology and trade secrets and invoked those charges as justification for the trade war with China. The Justice Department recently unveiled charges of racketeering and conspiracy to steal trade secrets against Huawei, one of China’s biggest telecom equipment makers, accusing it of trying to steal source code and other trade secrets from six American companies.

While a trade agreement reached between America and China early this year included pledges by Beijing to halt some of the practices that Washington has objected to, it did not allay the administration’s deep misgivings at the prospect of China’s candidate taking the top job at the intellectual property organization.

Peter Navarro, Mr. Trump’s trade adviser, has been critical of electing a Chinese official to run the intellectual property office. After the U.S.-China trade deal, Mr. Navarro has been focused on ensuring that the Chinese government keeps its promises to protect intellectual property. As part of that, he has been spearheading proposals to curb the flow of counterfeit products from China that are sold on American e-commerce platforms.

“We’re talking about over 100,000 packages a day coming into the U.S. from China that can defraud, harm or even kill Americans,” Mr. Navarro said in January.

He also raised the specter of growing Chinese influence across the United Nations organization. Control of its intellectual property office would have given China power over five of the U.N.’s 15 specialized agencies, Mr. Navarro noted.

The four already led by China include the Food and Agriculture Organization, the International Civil Aviation Organization, the Industrial Development Organization and the International Telecommunications Union. No other country was in charge of more than one, he said.

Alan Rappeport and Lara Jakes contributed reporting from Washington.