The United States should halt its “close-in” aerial and naval surveillance of China, a senior Chinese military officer told Susan E. Rice, President Obama’s national security adviser, on Tuesday.

Gen. Fan Changlong, vice chairman of the Central Military Commission, gave the warning on the last day of Ms. Rice’s visit to China, her first since she took up her post 15 months ago. It came with Chinese-American relations at their coolest in years.

General Fan told Ms. Rice that the United States should take the “correct” view of the development of the Chinese military, and “decrease and even end close-in ship and aircraft surveillance of China,” according to Xinhua, the state-run news service. American forces have watched China closely for decades.

The general’s remarks highlighted the wide gaps that have developed on a variety of issues between the countries since President Xi Jinping of China met with Mr. Obama in California in July 2013. Mr. Xi has steadily consolidated control at home since then, and China has vigorously pressed territorial claims in the South and East China Seas. It has enforced an antimonopoly law that some American corporations say favors Chinese champions, and taken other steps that have dismayed American businesses.

Ms. Rice stressed to her hosts the significance of her spending three days in Beijing when the United States has pressing concerns elsewhere. But her immediate task was limited: setting the agenda for Mr. Obama’s planned November visit. He will attend an Asia-Pacific Economic Cooperation summit meeting, then meet with Mr. Xi for a day.

Chinese officials appeared to have only modest expectations for Ms. Rice’s visit. “This cannot solve the problems,” said Shi Yinhong, professor of international relations at Renmin University. “Whether it’s matters of Japan, North Korea, Russia — there’s a long way to go.”

Wu Xinbo, director of the Center for American Studies at Fudan University in Shanghai, said friction had built since Mr. Obama went in April to Japan, South Korea, Malaysia and the Philippines, four countries that worry about Chinese regional ambitions. “The relationship has gotten worse,” Mr. Wu said. “There is a danger of it drifting further.”

In her public remarks in Beijing, Ms. Rice mentioned topics that offered some mutual interest but were removed from issues like China’s territorial claims and Washington’s complaints about China’s role in cybertheft.

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.

By JANE PERLEZ September 9, 2014 in The New York Times