"If a summit meeting is deemed as an important means in considering ways to resolve the abduction issue, we must take it into consideration as a matter of course in negotiating with them," Abe told a parliamentary committee.
The prime minister, responding to a question from an opposition lawmaker, was speaking the day after his senior aide arrived in Pyongyang on a surprise visit.
But Abe refused to comment on the purpose of Isao Iijima's trip to the reclusive state.
Some of those snatched were allowed to return to Japan along with children who were born in the North, but Pyongyang said the rest of them had died.
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However, many in Japan believe the North is still holding some and Pyongyang's perceived refusal to come clean has derailed efforts to normalise ties.
Iijima was also a senior aide to Koizumi and is known to have played a role in organising his trips to Pyongyang in 2002 and 2004 for talks with then North Korean leader Kim Jong-Il. Abe accompanied Koizumi on the 2002 visit.
Reports were rife with speculation that the North was trying to thaw icy relations with Japan at a time when ties with the US and South Korea have gone into deep freeze after nuclear and missile tests.
The United States, along with its two Asian allies, has increased pressure on Pyongyang to drop its nuclear ambitions and to join the international community.
Despite his wolfish tone, Abe has shown a pragmatic side in foreign relations, reaching out to South Korea and China during his first brief stint as prime minister.
Chief Cabinet Secretary Yoshihide Suga, Japan's top government spokesman, declined to discuss Iijima's visit.
He said that Tokyo stood firm on its mission to resolve the kidnapping issue as well as North Korea's military threats.
"Japan's North Korean policies are clear. With dialogue and pressure, we are working toward a comprehensive resolution of various issues, such as abduction, the nuclear issue and missiles," Suga told a regular press briefing.