Tokyo announced in July it was easing sanctions against Pyongyang, following its promise to re-investigate the cases of the abductees.
During their latest talks in China on Monday, the North Korean side said it was too early to report detailed results of the investigation, Abe told reporters.
But the North asked a Japanese envoy to visit Pyongyang to "meet members of the special investigation committee directly and hear about details of the current state of the probe", he said.
Japan believes dozens of people were snatched in the 1970s and 1980s to train the North's spies in the Japanese language and customs.
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Japanese officials had expected the report by September, but North Korea recently said it would be unable to supply substantial details by then.
North Korea admitted in 2002 that it had kidnapped 13 Japanese citizens to train its spies.
Five of the abductees returned home but Pyongyang said - without producing credible evidence - that the eight others had died.
That claim provoked uproar in Japan, where there are suspicions that dozens or perhaps even hundreds of others were taken.