Kim also pledged to work for a nuclear-arms-free Korean peninsula and a peaceful solution to a crisis over the North's nuclear programmes through multilateral talks, Junichiro Koizumi told a news conference on Saturday .
"We must normalise our abnormal ties," Koizumi said. "It is in the interests of both countries to change our hostile relation into a friendly one, our confrontational ties into cooperative ties. That is why I went to North Korea a second time."
The five abductees were ordinary young adults when they were snatched from their home towns a quarter of a century ago and taken to North Korea to help train spies.
They came back to Japan in October 2002, a month after Koizumi's first landmark summit with Kim, but had to leave behind their seven North Korean-born children, aged 16 to 22.
One of the returned abductees, Hitomi Soga, is married to a former US army sergeant, Charles Robert Jenkins, who also stayed behind in North Korea with their two daughters.
Koizumi said these four could meet in Beijing to discuss their future because Jenkins, who the United States says deserted 40 years ago, is worried he would be turned over to the US authorities if he came to Japan.
Koizumi agreed that Japan would provide impoverished North Korea with 250,000 tonnes of food aid and $10 million of medical supplies.
Kim Jong-il wants a nuclear-
weapon- free Korean peninsula
The official Korean Central News Agency (KCNA) said the talks marked "an important and historic event in restoring the confidence, improving the relations between the two countries and promoting peace and stability in Asia and the rest of the world".
Missing and dead?
The breakthrough in the emotional dispute over the abductees and their families could give Koizumi's popularity a boost ahead of a July election for parliament's Upper House.
Kim stunned the world at his first meeting with Koizumi in 2002 when he admitted to the kidnapping of 13 Japanese in the 1970s and 1980s. North Korea said eight of those were dead.
Japan says North Korea has kidnapped at least 15 Japanese and wants a convincing account of the fate of the other 10, including Megumi Yokota, who was 13 when she was abducted in 1977.
Koizumi said that Kim had agreed to a reinvestigation, but that might not be enough to satisfy their families back in Tokyo.
In a declaration signed by Koizumi and Kim at their last meeting, Kim pledged to uphold international treaties on nuclear issues and to extend a moratorium on ballistic missile launches.
Koizumi said Kim reaffirmed a moratorium on ballistic missile launches on Saturday.
"It is in the interests of both countries to change our hostile relation into a friendly one, our confrontational ties into cooperative ties. That is why I went to North Korea a second time"
North Korea shocked Japan in 1998 when it launched a test missile over Japan's main island and it is believed to have about 100 Rodong missiles that could hit Japanese cities.
Japan offered in the declaration to provide full-scale aid to the impoverished country once diplomatic ties were established.
Talks on establishing ties foundered after North Korea failed to clear up Japan's doubts over the fate of the remaining abductees and fresh concerns arose about its nuclear ambitions.
Talks in Beijing this month on North Korea's nuclear programme failed to narrow gaps between the two main protagonists, the United States and North Korea. The other participants were South Korea, Japan, China and Russia.