During a meeting with Mr. Xi at the Great Hall of the People, Ms. Rice said the two countries could work together to combat climate change and terrorism.

She discussed the possibility of China’s “making a contribution” in the fight against the Islamic State in Iraq and Syria. “The Chinese expressed interest in our proposal,” said a senior administration official traveling with Ms. Rice. “We are trying to build the international coalition that China should be part of. China’s answer was not ‘No.’ ”

The Pentagon announced in August that a Chinese fighter jet had flown perilously close to a Navy P-8 Poseidon surveillance plane off the southern coast of China, the fourth such encounter this year. In private meetings, Ms. Rice urged Chinese officials to come to a “better understanding” of how their military forces should act in international waters and airspace, the administration official said, adding that the Chinese officials understood the risks of intercepting and shadowing surveillance planes.

The official said Ms. Rice had raised human-rights cases, but declined to say if she had asked her hosts to let Gao Zhisheng, a dissident lawyer released from prison last month, join his wife in San Francisco. Discussing the cases publicly would be “counterproductive,” the official said.

The reticence was unusual, said Kenneth Roth, executive director of Human Rights Watch. “It’s quite extraordinary not even to mention the names of imprisoned dissidents whose names have been quietly raised,” he said. “It’s difficult to comment on whether there is something about these particular discussions that require such unusual discretion, but I’m skeptical.”

The last day of Ms. Rice’s visit coincided with the end of a visit by Jimmy Carter, who as president established diplomatic relations with China. He toured several cities and gave speeches, mostly to university students.

His reception was reserved, reflecting tensions with America but out of keeping with his place in history, said Orville Schell, director of the Center on U.S.-China Relations at the Asia Society in New York, who was at several events with Mr. Carter. Some locations were changed at the last minute, and there were empty seats at a banquet for him at the Great Hall of the People, hosted by Vice President Li Yuanchao.

“I was surprised the Chinese government did not do more to highlight the importance of improving relations by President Carter,” Mr. Schell said.