The National Security Agency has sought to create back doors into the networks of Chinese telecommunications giant Huawei Technologies in an effort to learn whether the company was spying on behalf of Beijing, according to a leaked document.

The agency also apparently hoped to take advantage of the presence of Huawei equipment in the networks of other countries of interest, such as Iran, Afghanistan, Pakistan, Kenya and Cuba, according to the document leaked by former agency contractor Edward Snowden.

The document was obtained and published by the New York Times on its Web site Saturday. The newspaper said that other documents it obtained showed that the NSA “pried its way into the servers” of Huawei at its headquarters in Shenzhen, China, obtained data about how the company’s routers worked and monitored the communications of the company’s top executives.

The classified 2010 document stated: “Many of our targets communicate over Huawei-produced products, we want to make sure that we know how to exploit these products — we also want to ensure that we retain access to these communication lines, etc.”

The report comes after nine months of disclosures about NSA surveillance based on documents leaked by Snowden that have greatly diminished trust in the agency and hurt American tech companies that cooperate under court order with the NSA.

It also comes as the Obama administration has sought to advance talks with China on reducing cyber-conflict and industrial cyber-espionage. For several years, the United States has been concerned about Chinese hacking of U.S. industry to steal commercial and military secrets.

Huawei in particular has been a lightning rod for those concerns. In 2012, House Intelligence Committee leaders released a report concluding that Huawei and another Chinese tech company posed a risk to U.S. national security because of their ties to the Chinese government and recommended that U.S. firms avoid using their equipment.

On Saturday, NSA spokeswoman Vanee Vines said in a statement that the agency’s activities “are focused and specifically deployed against — and only against — valid foreign intelligence targets in response to intelligence requirements.”

She said that the United States does not “steal the trade secrets of foreign companies on behalf of — or give intelligence we collect to — U.S. companies to enhance their international competitiveness or increase their bottom line.”

Referring to the leaked document, Vines also asserted that “continuous and selective publication of specific techniques and tools used by NSA to pursue legitimate foreign intelligence targets is detrimental to the security of the United States and our allies — and places at risk those we are sworn to protect.”

Reached for comment, Huawei vice president for external affairs William Plummer said: “We have been challenged for years now to prove a negative about ourselves when, frankly, if there is truth to what is said, they already know the company is innocent and independent.”

James A. Lewis, a senior fellow at the Center for Strategic and International Studies who has led back-channel cyber-talks between U.S. and Chinese officials, said he doubts that the latest revelation will affect those discussions.

“The Chinese always believed that the U.S. was hacking into everything, so Snowden’s revelations weren’t a big surprise to them,” Lewis said.

On the military front, he said, “the Chinese don’t want conflict any more than we do and would like to find a way to make [cyberspace] more stable.” But on commercial espionage, he said, “they don’t have any interest in making concessions. They told us that before the Snowden leaks. They told us that during the Snowden leaks.”