Kim Jong-un's sister says Japanese Prime Minister Fumio Kishida offered to meet with the North Korean leader "as soon as possible", but stressed there would be conditions.
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In a parliamentary session, Kishida said a meeting with Kim is "crucial" to resolve the issue of abductions of Japanese nationals, a major sticking point in bilateral ties.
Kim's sister and senior official, Kim Yo-jong, said in a statement on Monday that Kishida recently used an unspecified channel to convey his position that he wants to meet Kim Jong-un in person "as soon as possible".
She said there will be no breakthrough in North Korea-Japan relations as long as Kishida's government is engrossed in the abduction issue and interferes in the North's "exercise of our sovereign right", apparently referring to its weapons testing activities.
"The history of the DPRK-Japan relations gives a lesson that it is impossible to improve the bilateral relations full of distrust and misunderstanding, only with an idea to set out on a summit meeting," Kim Yo-jong said, using the abbreviation of the North's official name, the Democratic People's Republic of Korea.
"If Japan truly wants to improve the bilateral relations and contribute to ensuring regional peace and stability as a close neighbour of the DPRK, it is necessary for it to make a political decision for strategic option conformed to its overall interests," she said.
In February, Kim Yo-jong issued a similar statement on bilateral ties, saying North Korea was open to improving relationships with Japan and even inviting Kishida to Pyongyang.
But she said those would be possible only if Tokyo stops taking issue with North Korea's legitimate right to self-defence and the abduction issue.
After years of denial, North Korea acknowledged in an unprecedented 2002 summit between Kim Jong-il, the late father of Kim Jong-un, and then-Japanese prime minister Junichiro Koizumi that its agents had kidnapped 13 Japanese, mainly to train spies in Japanese language and culture.
It allowed five of them to return to Japan that year, but said the others had died. Japan thinks at least some of them may still be alive, and believes hundreds more may also have been abducted.
North Korea and Japan had been scheduled to play a World Cup qualifier on Tuesday in Pyongyang, but FIFA, soccer's governing body, said on Saturday it cancelled the match.
North Korea recently said it couldn't host Japan and requested a neutral venue "due to unavoidable circumstances", according to the Asian Football Confederation.
Earlier on Monday, North Korea's state media reported that Kim Jong-un supervised a tank exercise and encouraged his armoured forces to sharpen war preparations in the face of growing tensions with South Korea.
Australian Associated Press