"China has been very clear about what its long-term goals are strategically," James Jones, who served as NSA under former President Barack Obama, told CNBC's Hadley Gamble. "We need to take that very seriously."
One Chinese goal is "total control of their own people using technology," he said at the Atlantic Council Global Energy Forum in Abu Dhabi on Sunday. "They're making astonishing progress to control every single citizen, whatever he or she does."
"They're giving grades for citizenship, which will affect their jobs you're going to hold, the travel you can do and everything else," he added, seeming to refer to China's social credit system. "Where they're moving is scary," he said. "They obviously want to export that to other countries."
He said Beijing is using a "Trojan horse" strategy to gain influence in "many parts of the world."
"They penetrate the economies, they buy up everything they can, pay off everybody they can...get a chokehold on the economy as much as they can and then make demands for the behavior of the government," he said.
That's something the U.S. should address, said Jones.
"One of the things that concerns me a little bit is that we've stopped talking about values in the world...even in the democratic countries. We should talk about human rights," he said.
Asked if the U.S. should support protesters in Hong Kong even if it puts trade talks with China at risk, Jones said: "Is trade more important than human values?"
He noted that the U.S. didn't trade with the Soviet Union during the Cold War until the Berlin Wall came down and the regime collapsed. "But in China's case, we were asleep at the switch," he said. "They were making astonishing progress, and all of a sudden they're pure competitors."
"I'm not sure that we really understand the degree to which China is strategically intent on replacing the United States as the most dominant culture in the world," he said.
Jones also said the U.S. should compete with China "everywhere they are in the world, including Africa and other places."
Competing on technology is "more serious", but the U.S. "can win," he predicted.
Referring to next-generation wireless networks, he said: "If China successfully captures the infrastructure aspects of the 5G emergence...that affects the GDP of countries significantly, anywhere from 1.5% to 2.5%."
"This is a competition that I think the United States can win, because we have a completely different philosophy about what the 5G world will look like," he said.
"We have a completely different marketing strategy...I think we're going to be successful."
—CNBC's Evelyn Cheng and Shirley Tay contributed to this report.