The husband of Japanese abductee Hitomi Soga is said to have expressed hope that his family will stay together.
The family have met the Japanese ambassador in Jakarta
Charles Jenkins, an alleged US army deserter living in North Korea, was reunited with his wife on Friday.
Ms Soga had not seen Mr Jenkins or their two children since 2002, when she returned to Tokyo with other Japanese kidnapped by North Korea in the 1970s.
Ms Soga wants her family to live in Japan, but Mr Jenkins has previously refused, fearing extradition to the US.
The family met in Indonesia, which unlike Japan has no extradition treaty with the US.
Japanese government spokesman Kyoko Nakayama said Mr Jenkins had told her over the weekend that he wanted the family to stay together.
But exactly where they will live if they do decide to remain in the same country is still unclear.
Hiroshi Oguma, a Japanese spokesman, said the family was not under any pressure to make a quick decision. The booking at their Jakarta hotel - paid for by the Japanese government - is open-ended.
Since Friday, the family have only left their hotel suite once - to dine
with the Japanese ambassador to Indonesia.
Much of the rest of their time has been spent talking, eating and
watching television, according to government officials.
"This morning they watched a Harry Potter movie in English
with Korean subtitles," said Hiroshi Oguma.
Media reports talk of the two daughters struggling to come to terms with their five-star hotel accommodation. Neither Mika, 21, nor Belinda, 18, have ever left Stalinist North Korea before.
Mr Jenkins' and Ms Soga's enforced separation has been given wide and sympathetic coverage by the Japanese media.
Friday's emotional reunion on the tarmac at Jakarta International Airport was watched avidly by the Japanese public.
Snatched in the '70s and '80s
Used as cultural trainers for N Korean spies
Five allowed home in 2002
Five children now freed from N Korea
Eight said to be dead, others missing
The couple hugged and
kissed each other, before the family boarded a bus to take them to their hotel.
Ms Soga first met her husband in Pyongyang, after her abduction by North Korean agents in 1978 to act as a cultural trainer for the country's spies.
She was allowed to go back to Japan in October 2002, following a high-profile visit to Pyongyang by Japan's Prime Minister Junichiro Koizumi.
But Mr Jenkins stayed behind with Belinda and Mika, fearing extradition to the US.
Mr Jenkins went to North Korea in 1965, while leading a patrol in South Korea near the Demilitarized Zone (DMZ). He told his platoon he was going to investigate a noise.
The US Army says he deserted, but relatives in the US believe that he, like Ms Soga, was kidnapped.
But US Secretary of State Colin Powell has made it clear that the American authorities are still taking outstanding charges against him seriously.