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The differences over his security aside, leaving Mr. Chen in China is risky for President Obama. Washington now will be seen as party to an agreement on Mr. Chen‘s safety that it does not have the power to enforce.

Ai Xiaoming, a documentary filmmaker and activist, said the Chinese government fails to ensure people’s rights, so the best solution would be for Mr. Chen and his family to go to America.

“In the first place, ChenGuangcheng should not have to ask a foreign country to protect his rights. His rights should be protected by his own country, through the constitution. But it is obvious that this cannot be done,” Mr. Ai said. “I feel that the U.S. has always accepted political refugees, it has always provided asylum, so I hope to see ChenGuangcheng safely leave.”

Mrs. Clinton said in a statement that Mr. Chen‘s exit from the embassy “reflected his choices and our values” and said the U.S. would monitor the assurances Beijing gave. “Making these commitments a reality is the next crucial task,” she said.

The discrepancies also muddy an agreement that would have shelved, at least temporarily, a predicament that threatened to move human rights to the front of a U.S.-China agenda crowded with disagreements over trade imbalances, North Korea and Syria.

With Mr. Chen out of the way, in theory, Mrs. Clinton, Treasury Secretary Timothy F. Geithner and their Chinese counterparts would be set to focus on the original purpose of their two-day talks starting Thursday: building trust between the world’s superpower and its up-and-coming rival.

Even so, the Chinese Foreign Ministry signaled its pique with the affair, demanding that the U.S. apologize, investigate how Mr. Chen got into the embassy and hold those responsible accountable.

“What the U.S. side has done has interfered in the domestic affairs of China, and the Chinese side will never accept it,” Foreign Ministry spokesman Liu Weimin said in a statement.

Senior U.S. officials, speaking on condition of anonymity to discuss the intense negotiations that led to Mr. Chen‘s leaving the embassy, said the U.S. helped Mr. Chen get into the embassy because he injured his leg escaping from his village. In the embassy, Mr. Chen did not request safe passage out of China or asylum in the U.S., the officials said.

The officials refused to say if Washington would apologize. One official said that embassy staff acted “lawfully” and in conformity with policy, suggesting that the U.S. does not believe it has anything to apologize for.

The arrangements for Mr. Chen carries risks as well for China‘s government, which worries about encouraging activists and government critics.

As news spread that he had been taken to the hospital, in the eastern part of the city, media crews and a few supporters gathered outside. A man stood in front of the gate at the hospital and held up a sign saying, “Freedom for Guangcheng, Democracy for China,” for a minute before police took him inside. The hospital’s name became a banned search term on the much-censored Chinese Internet, joining a long list of permutations for Mr. Chen’s name.

The U.S. officials said Mr. Chen would be settled outside his home province of Shandong and have several university options to choose from. They also said the Chinese government had promised to treat Mr. Chen “like any other student in China” and would investigate allegations of abuse against him and his family by local authorities.

Associated Press reporters Charles Hutzler and Gillian Wong contributed to this report.