"I support this as a first step to the comprehensive resolution of issues concerning North Korea."
Kim and Trump signed a document after their talks in which the North Korean leader reaffirmed his commitment to "work toward complete denuclearisation of the Korean Peninsula", without giving further details.
The document also refers to the repatriation of the remains of prisoners of war and those killed in conflict, but makes no specific reference to people abducted by North Korea.
The Japanese government has officially listed 17 people as abductees, but there are strong suspicions that dozens more citizens were snatched to train Pyongyang's spies in the Japanese language and culture.
Japan has repeatedly called for the issue to be raised in discussions with Pyongyang, and Trump said at a press conference on this afternoon that he had discussed the issue with Kim.
"I highly appreciate the fact that President Trump firmly touched upon what I told him recently about the abduction issue which is very important to us, to Japan," Abe said.
"I want to hear the details by phone (from Trump). I will continue aiming to resolve concerns such as the abduction, nuclear and missile issues," he added.
Japan has maintained a hardline position on North Korea despite a whirlwind of diplomacy towards Pyongyang in recent months, and has been left largely on the sidelines as South Korea and the United States have held talks with Kim.
Abe has suggested recently he could talk with Kim directly in an attempt to resolve the abduction issue, though there has been no substantive movement thus far on potential talks.
"From now on, there will be various kinds of bargaining toward a Japan-North Korea summit," the unnamed official said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)