"North Korea will receive relief only when it shows verifiable and irreversible steps to denuclearisation", Mattis said during public remarks at a meeting with the South Korean and Japanese defence ministers.
"We will continue to implement all U.N. Security Council resolutions on North Korea", Mattis said as he wrapped up a visit to Singapore Sunday.
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.
Washington wants North Korea to quickly give up all its nuclear weapons in a verifiable way in return for sanctions and economic relief.
"We can anticipate, at best, a bumpy road to the negotiations", the defense secretary added.More news: Melania Trump will not travel to Singapore summit or G7
In the statement, Defense Minister Itsunori Onodera and his US and South Korean counterparts, Jim Mattis and Song Young Moo, confirmed that their common goal is North Korea's complete, verifiable and irreversible denuclearization.
South Korean Defense Minister Song Yong-moo (L) and his American counterpart Jim Mattis walk out of a room after talks in Singapore on June 2, 2018 in this photo provided by Song's ministry.
The Singapore meeting was the first three-way talks between them since last October, when they gathered in Clark, the Philippines, for the ASEAN Defense Ministers' Meeting-Plus.
Meanwhile, North Korea moved to replace its defense minister ahead of the pivotal negotiations, Japan's Asahi newspaper reported Sunday, citing people that it didn't identify.
And Japan's defense minister said the three countries need to strengthen their military cooperation, but also called on North Korea to cooperate in resolving long-standing humanitarian issues like the Japanese nationals abducted by the regime.More news: Apple Aims To Help Parents Crack Down On Kids' iPhone Use
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.
Song says allies must be cautious, but some of Pyongyang's recent steps are reasons to be optimistic.
North Korea has criticized South Korea's participation in joint multinational exercises, saying it runs counter to the Panmunjeom Declaration announced after the inter-Korean summit in April.
Onodera and Song were to hold bilateral talks separately later Sunday.
Song said South Korea will cooperate closely with the U.S.in pushing for measures to ease inter-Korean military tensions and build mutual confidence.More news: Serena Williams withdraws from French Open clash with Maria Sharapova