The US has stressed it will seek the extradition of an alleged army deserter when he travels to Japan for health care.
Mr Jenkins disappeared during army service in South Korea in 1965
Charles Jenkins, 64, has been living in North Korea since the 1960s, previously refusing to join his wife in Japan for fear if being turned over to the US.
But he decided to go ahead with the trip after signs that the US would not seek custody while he was in hospital.
Tokyo said Mr Jenkins would be moved to a Japanese hospital on Sunday.
Washington stressed that it was still intent on pursuing Mr Jenkins.
"Our view is that Sgt Jenkins... is a deserter from the US Army. He has been charged with extremely serious offences," said US State Department spokesman Richard Boucher on Thursday.
"Once he is in Japan, he becomes subject to the terms of the US-Japan status of forces agreement and falls under the authority of the US military," he said.
Asked whether Washington would give priority to his medical treatment, Mr Boucher said: "I think we'll just have to see how the medical situation evolves.
"We're going to take this one step at a time and see what happens."
Earlier on Thursday the US ambassador to Japan, Howard Baker, said his government was "sympathetic" to Mr Jenkins' health problems, while Japanese government officials said they did not expect Washington to press for custody which he was being treated.
He reportedly needs urgent medical attention for a serious stomach condition, following surgery in Pyongyang.
Japan's Chief Cabinet Secretary Hiroyuki Hosoda said that Mr Jenkins'
condition was serious.
"It's an emergency measure for the purpose of saving human life. We are not saying (Jenkins) is in a critical condition, but we cannot leave him as he is now," he said.
Mr Jenkins is currently in Jakarta - the venue of a dramatic reunion last week with his Japanese wife, Hitomi Soga.
Ms Soga, who was kidnapped by North Korean secret agents in the 1970s, met and married Mr Jenkins in Pyongyang in 1980. They had not seen each other since 2002, when Ms Soga was allowed to return to Japan.
Jakarta was chosen as a reunion venue because Indonesia has no extradition treaty with Washington.
Mr Jenkins has indicated he would like to move to Japan permanently to be with his wife and their two daughters.
He has been in North Korea since 1965, after disappearing from patrol in South Korea near the Demilitarized Zone (DMZ). He told his platoon he was going to investigate a noise and never came back.
The US Army says he deserted, but relatives in the US believe that he, like Ms Soga, was kidnapped.