WASHINGTON — The Obama administration rushed to contain a growing diplomatic crisis between the United States and China, sending a senior diplomat to Beijing to discuss the fate of a blind dissident who fled house arrest last week.


Amid intense secrecy, including a nearly blanket refusal to comment, the administration sought to negotiate over the safety of the dissident, Chen Guangcheng, who is said to be in American hands in Beijing — though it remained unclear late Sunday whether he was in the embassy, in a diplomatic residence, or somewhere else.


The senior diplomat, Kurt M. Campbell, an assistant secretary of state, arrived Sunday to meet with Chinese officials concerning Mr. Chen’s case, and to try to keep the matter from undermining the administration’s longstanding effort to improve economic and security relations with China, senior officials and diplomats in Washington and Beijing said.


A senior American official said that China’s leadership met Sunday to work out their response to Mr. Chen’s escape before scheduled meetings this week with Secretary of State Hillary Rodham Clinton and Treasury Secretary Timothy F. Geithner. Mrs. Clinton is due to leave Washington for China on Monday night.


“They’re trying to figure out what they’re going to tell Hillary Clinton,” the official said of the Chinese leaders, speaking on the condition of anonymity because of the diplomatic delicacy surrounding the case. “We’d like to know as much as we can before she leaves.”


The administration’s effort to contain the crisis — the State Department declined to confirm that Mr. Campbell was in China, even though he was photographed in a Marriott hotel in Beijing — underscored the political challenge facing President Obama, at home and abroad.


“This is the greatest test in bilateral relations in years, probably going back to ’89,” said Christopher K. Johnson, until recently a senior China analyst at the Central Intelligence Agency, referring to the year of the crackdown on student protests in Tiananmen Square. He noted that the relationship had weathered tense moments since then, like the forced landing of a Navy spy plane on Hainan Island in 2001 after a midair encounter with a Chinese fighter jet.


Mitt Romney, the presumptive Republican presidential nominee, called for the administration to “take every measure” to protect Mr. Chen and his family. While he did not address the handling of the case, he said the matter demonstrated the need for unflinching American support for human rights in China.


“Any serious U.S. policy toward China must confront the facts of the Chinese government’s denial of political liberties, its one-child policy and other violation of human rights,” Mr. Romney said in a statement on Sunday, his first remarks on the issue since Mr. Chen’s escape was reported Friday.


Mr. Chen, 40, became famous because of his strong opposition to forced abortions and sterilizations conducted as part of China’s policy of limiting families to one child per couple. “Our country must play a strong role in urging reform in China and supporting those fighting for the freedoms we enjoy,” Mr. Romney said.


The administration’s only public comment so far on Mr. Chen’s case came from an unexpected source: Mr. Obama’s top counterterrorism adviser, John O. Brennan. Asked about the matter on “Fox News Sunday,” he declined to discuss Mr. Chen’s whereabouts in any detail, but he acknowledged that “we are working very closely with the individuals involved in this.”


He went on to say that the administration sought “an appropriate balance” when advocating for human rights in strategically important countries like China.


“I think, in all instances, the president tries to balance our commitment to human rights, making sure that the people throughout the world have the ability to express themselves freely and openly,” Mr. Brennan said, “but also that we can continue to carry out our relationships with key countries overseas.”