Japan offered a cool response to the North Korean leader's sister's offer to enhance bilateral ties on Friday.
Prime Minister Fumio Kishida has said he wants to change the relationship between Tokyo and Pyongyang, and Kim Yo Jong hinted on Thursday at a possible future invitation for the Japanese leader to visit North Korea.
Tokyo's top government spokesman said only that Japan was "paying attention" to Kim Yo Jong's comments.
"Kishida has said he wants to have negotiations... towards realizing a summit with President Kim Jong Un," Yoshimasa Hayashi told reporters on Friday.
However, North Korea's "argument that the abduction issue has been resolved is fully unacceptable," he said.
Kim Yo Jong said in a statement on Thursday that relations had deteriorated "since Japan has persistently raised as a precondition (to talks) the abduction issue, which had already been settled."
However, the statement also said: "There will be no reason for the two countries not to become close and the day of the prime minister's Pyongyang visit might come."
North Korea admitted in 2002 that it had sent agents to kidnap 13 Japanese people in the 1970s and '80s who were used to train spies in Japanese language and customs.
The abductions remain a potent and emotional issue in Japan and suspicions persist that many more were abducted than have been officially recognized.
Contention over the issue could hinder progress toward a summit between Kishida and Kim Jong Un, said Masao Okonogi, a North Korea expert and professor emeritus of Keio University.
"It looks unlikely that things will move forward soon," he said, because "there's no benefit to Japan in holding a summit" if North Korea wants to ignore the abduction issue.
That was echoed by Daisuke Kawai, deputy director of the University of Tokyo's economic security research program, who said there was a "clear misalignment" between the two countries on the issue.
"North Korea likely expects something in return for addressing the abduction issue," he told AFP.
"But there is nothing Japan can currently offer that would satisfy North Korea's demands without significant concessions, such as recognizing North Korea's nuclear and missile programs or easing sanctions."
Kishida expressed his wish to meet with North Korea's leader "without any conditions," saying in a speech at the U.N. General Assembly last year that Tokyo was willing to resolve all issues, including the kidnappings.
Kim Yo Jong's statement came days after Seoul announced it was restoring diplomatic ties with Cuba, a longtime ally of North Korea, which had been broken off since 1959.
Kishida, whose nation has no formal diplomatic ties with Pyongyang, has said he was exploring possibilities to meet North Korea's leader to resolve the matter of Japanese civilians abducted in the 1970s and 1980s.
Kim Yo Jong, a deputy department director in the ruling Workers' Party, said Kishida's comments could be considered positive if meant to advance relations.
"If Japan... makes a political decision to open a new path for improving ties based on mutual respect and respectful behavior, it is my view that the two countries can open a new future," she was quoted as saying.
Japan has been critical of North Korea's pursuit of ballistic missiles and nuclear weapons, often drawing harsh rebukes from Pyongyang, especially as Tokyo stepped up its security alliance with South Korea and the United States.
Kim added her view was a personal observation and, as far as she knew, the North's leadership had no specific plans for its relations with Japan or to make contact with Tokyo, KCNA said.
Kim is widely considered the closest confidant and adviser to her brother on external policy matters.
U.S. Senior Official for North Korea Jung Pak told reporters Washington supports any diplomacy with Kim's government, which has not responded to repeated U.S. offers to engage in talks without preconditions since President Joe Biden took office in 2021.
"They've shut their borders since January 2020 and we support... any diplomacy there," Pak said in a briefing at the State Department.
"Any kind of diplomacy that DPRK does, that's not Russia, is a positive thing," she said about Pyongyang's growing cooperation with Moscow that has alarmed Washington.
Another U.S. official has said Washington wanted Japan to ensure it had "smoothed over" a possible meeting between Kim and Kishida with South Korea. The U.S. has worked to develop a three-way coordination of policy on North Korea and other security issues between itself, Japan and South Korea.
Pak said she could not say whether North Korea's willingness to speak to Japan could be linked to Seoul's recent move to establish diplomatic ties with the North's longtime ally Cuba, but added: "I think Pyongyang has always been interested in driving a wedge in our relationships or in the relationships between Japan and other countries and Korea and other countries."
Japan’s former Prime Minister Junichiro Koizumi paid a landmark visit to Pyongyang in 2002, and met Kim’s father Kim Jong-il.
His visit led to the return of five Japanese nationals and a follow-up trip by Koizumi, but the diplomacy soon broke down, following Tokyo’s claim that Pyongyang was not coming clean about the abduction victims.