Regional allies of the USA expressed their concerns over Trump potentially arranging a deal with Kim that would see North Korea surrender its long-range missiles for sanctions relief but keep its short-range weapons, according to the report.
But analysts say North Korea will be unwilling to cede its nuclear deterrent unless it is given security guarantees that the USA will not try to topple the regime.
His comments came after Trump on Friday conceded that North Korea would not agree immediately to give up its nuclear arsenal, and seemingly walked back expectations for a quick deal from his planned June 12 meeting in Singapore with Kim.
The South Korean government of liberal President Moon Jae-in has made it a top priority to engage the North in dialogue to resolve decades-old animosity and bring lasting peace, publicly pledging it would never pursue the collapse of its neighbor.
"As defense ministers we must maintain a strong, collaborative defensive stance so we enable our diplomats to negotiate from a calm position of strength in this critical time", Mattis said.
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South Korea's Defense Minister Song Young-moo (L) poses for a photo with his American and Japanese counterparts - Jim Mattis (C) and Itsunori Onodera - before a trilateral meeting on the sidelines of the 17th Asian Security Summit in Singapore on June 3, 2018.
"In light of how North Korea has behaved in the past, I believe it is important not to reward North Korea exclusively for agreeing to have a dialogue". It was the first time since October previous year for the Japanese, U.S., and South Korean defense chiefs to hold trilateral talks.
U.S. and North Korean officials continue to lay the groundwork ahead of the expected summit between U.S. President Donald Trump and North Korean leader Kim Jong Un.
"Of course, given North Korea's past, we must be cautious in approaching this", he added that some of the regime's recent actions "give us reasons to be positive and one can be cautiously optimistic as we move forward".
The summit was resurrected after Trump called it off in a letter to Kim on May 24, complaining of "the tremendous anger and open hostility" in comments from North Korea.
Song was quoted by the official as telling Onodera that given the rapid pace of developments on the Korean Peninsula, South Korea wants to cooperate with Japan to achieve the complete denuclearization of North Korea.