Mr. Liu, 61, was sentenced late in 2009 to 11 years in prison on charges of inciting subversion, a year after he was detained on the cusp of issuing a bold democratic petition called Charter 08. In 2010, he was awarded the Nobel Peace Prize, infuriating the Chinese government.

The prison authorities revealed late last month that Mr. Liu had advanced liver cancer and had been given medical parole. He has been receiving treatment in the university hospital in Shenyang, a city 390 miles northeast of Beijing, guarded by the police. He and his wife, Liu Xia, have not spoken publicly or received well-wishers outside their immediate family.

But a lawyer for Mr. Liu and friends of the couple have said the couple wanted Mr. Liu to go abroad for treatment, apparently out of distrust of Chinese hospitals and to give Mr. Liu some freedom in his final days.

Their efforts received a boost over the weekend after the American and German cancer specialists examined Mr. Liu on Saturday and said he was well enough to travel.

Dr. Joseph M. Herman of the MD Anderson Cancer Center of the University of Texas and Dr. Markus Büchler of the University of Heidelberg were invited by the Chinese government to examine Mr. Liu. But they apparently departed from the government’s official script that Mr. Liu was not stable enough to travel.

“While a degree of risk always exists in the movement of any patient, both physicians believe Mr. Liu can be safely transported with appropriate medical evacuation care and support,” the two doctors said in a joint statement on Sunday. “However, the medical evacuation would have to take place as quickly as possible.”

But the two doctors were also used in Chinese propaganda. They were shown visiting Mr. Liu in a video that appeared to have been made and issued with the backing of the Chinese authorities. The video released Sunday showed them and a number of Chinese medical workers crowded around Mr. Liu, gaunt and motionless in a bed, while a woman with short hair — apparently his wife, Liu Xia — stood at his feet.