"As a result of the Japan-North Korea talks, the North Korean side promised to the Japanese side that it will make a comprehensive and overall investigation into all the Japanese, including abduction victims and missing people whose possibility of being abducted cannot be ruled out," Abe told reporters.
"In keeping with the promise, it will set up a special commission for the investigation."
North Korea outraged Japan when it admitted more than a decade ago that it had kidnapped 13 Japanese in the 1970s and 1980s to train its spies in Japanese language and customs.
The issue is a highly-charged one in Japan, where there are suspicions that perhaps dozens of other people were taken.
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"Our mission will never end until the day comes when families of all abduction victims are able to embrace their children with their own arms," Abe said.
"We have tackled the problem with this determination and we hope that this will be the first step toward... An overall solution."
While relations with South Korea remain testy, Pyongyang's approach to its dealings with Japan appears to have softened in recent months, especially on the emotive issue of the abductions.
The two sides held a three-day meeting in Stockholm this week, building on official talks in China in March.