Speaking at a news conference closing out two days of economic and security talks that have been overshadowed by Mr. Chen’s case, Mrs. Clinton said she was encouraged by a statement earlier on Friday from China’s Foreign Ministry that said Mr. Chen could apply to study outside China. The proposal appeared to offer the possibility of a breakthrough in the crisis.

Mrs. Clinton said that progress had been made “to help him have the future that he wants” and referred to the ministry’s statement as well as a visit by American Embassy staff and an American doctor to Mr. Chen in a Beijing hospital on Friday, the first time they were able to see him in person since late Wednesday…

The announcement came hours after Mr. Chen, in a four-point statement conveyed by telephone to a friend, insisted that he did not want to seek political asylum in the United States but that he had been invited to attend New York University and hoped “to go to the United States and rest for several months.”

That would give Chinese officials a face-saving opportunity to allow Mr. Chen and his family to leave China, according to Jerome A. Cohen, a New York attorney and expert on Chinese law who discussed the proposal with Mr. Chen this week.