Over informal, private meals with American leaders, China’s Xi Jinping let his guard down a little. It was a decade ago, relations were less strained, and Mr. Xi, still cementing his power, hinted he worried about the Chinese Communist Party’s grip.

Speaking privately with President Barack Obama and Vice President Joe Biden, Mr. Xi suggested that China was a target of “color revolutions,” a phrase the party adopted from Russia for popular unrest in the name of democracy and blamed on the West. The recent “Arab Spring” uprisings across the Middle East had reinforced his concerns that China was vulnerable to public anger over corruption and inequality, both of which the country had in abundance.

“Xi couldn’t have been more forthright that China is beset by malevolent forces and internally prey to centrifugal forces,” said Daniel R. Russel, a former senior American diplomat who accompanied Mr. Biden to China in 2011.

“He would talk all the time about color revolutions. That’s clearly a sort of front-of-mind issue for him,” said Ryan Hass, the National Security Council director for China when Mr. Xi later visited the White House.