North Korea admitted in 2002 to kidnapping 13 Japanese civilians including Megumi during the 1970s and 1980s to train its spies in the Japanese language and customs.
It returned five victims and their families in 2002 but said the rest were dead.
Japan has rejected North Korea's account including that Megumi had killed herself as an adult in 1994.
|Cheney met the Yokota family at the request |
of the Japanese government [Reuters]
During talks with Abe on Wednesday, Cheney said the US wanted to see a resolution of what he called "the tragic case of Japanese abductees".
"I know it means a great deal to the Japanese people," he told the Yokota family.
Tokyo is demanding more information about the fate of the eight and others it says who were also kidnapped, and wants any survivors to be sent home.
Last year, Sakie Yokota met George Bush, the US president, and testified before American legislators.
She said the kidnappings were an international issue because North Korea had also kidnapped civilians from other countries.
"I'm just one mother, trying to get her child, who's been caught up in a kind of no-man's land, back to the place where she belongs," Sakie told Reuters last November.
Abe, who built his career on the emotionally-charged issue, has refused to provide aid to North Korea under the six-nation nuclear pact signed in Beijing last week unless the issue was addressed.
South Korea and China have been annoyed by Japan's insistence on including the abduction issue during the Beijing talks which they said should focus foremost on North Korea's nuclear weapons.
Critics say Japan's position could see it being isolated if progress was made toward North Korean denuclearisation.