Secretary of State Hillary Rodham Clinton speaks Monday during a luncheon hosted by the American Chamber of Commerce in Hong Kong. (Jerome Favre/BLOOMBERG)

Secretary of State Hillary Rodham Clinton tried to reassure China — the largest holder of U.S. Treasury securities — and other Asian countries Monday about the roiling debt debate in Washington even as she urged them to adopt fair competition principles at the core of the American economy.

“Many have questions about how the United States is going to resolve our debt ceiling challenge,” Clinton said in a speech in Hong Kong, the financial hub of Asia. “Let me assure you we understand the stakes. We know how important this is for us and how important it is for you.”

Clinton’s talk was notable for its prodding tone, urging countries to adopt economic rules of transparency, openness and fairness. And while Clinton mostly avoided direct mention of China, much of her sharpest words seemed aimed at the country, whose rapidly growing economy embodies all the problems highlighted by Clinton — loose government regulation, unfair competition by state-owned enterprises and widespread intellectual property theft.

“We all recognize the temptation to bend them,” Clinton said, referring to fair trade principles. “Some nations are making short-term gains doing just that. . . . And a number of nations — wealthy in the aggregate but often poorer per capita — might even think the rules don’t yet apply to them.”

Clinton’s words highlighted the complex, intertwined and sometimes antagonistic relationship between the U.S. and China. While China eagerly and aggressively competes with the U.S. in almost every field, it is also the largest foreign holder of U.S. dollar debt.

As a result, the current stalemate in Washington has not only threatened to push the U.S. government into default and downgrade its AAA rating, but it has put an enormous pool of Chinese investment at risk.

“I’ve had several meetings where the Chinese have basically made clear that they’ve made a substantial investment in the U.S.,” said a senior State Department official, who was not authorized to speak by name. “And they expect, not hope, expect that U.S. will abide by its various financial international commitments.”

Hours after she spoke, Clinton crossed into mainland China to meet with State Councilor Dai Bingguo.

According to U.S. officials accompanying her but not authorized to speak publicly, her discussion with Dai included the recent conflicts over disputed territories in the South China Sea, in which China has played an aggressive role, and the recent resumption of dialogue between North and South Korea over nuclear disarmament.

Clinton and Dai met for four hours, with the meeting running long because of the intensity of the issues they wanted to cover. According to the U.S. officials, Clinton asked Chinese leaders to use any influence they have with the North Koreans to persuade them to take seriously the meeting this week in New York between North Korea’s vice foreign minister and U.S. officials. The U.S. diplomats also expressed concern that North Korea might be contemplating future provocations, the officials accompanying Clinton said.

Clinton and Dai also talked about Vice President Biden’s upcoming visit with Xi Jinping, expected to be China’s next leader. The Chinese complained to Clinton about the Dalai Lama’s recent visit with Obama and about potential arms sales to Taiwan.