In a joint declaration issued Wednesday, Moon and Kim reaffirmed their commitment to completely rid the Korean Peninsula of nuclear weapons.

In an apparent gesture to partly answer the United State's demand for more denuclearization steps, the North Korean leader agreed to permanently dismantle the country's missile testing site and launch pads in Dongchang-ri.

He also offered to permanently dismantle the Yongbyon nuclear facility in exchange for certain "corresponding measures" from the US

The US is reportedly demanding a list of North Korea's nuclear arsenal and means to verify it.

North Korea, on the other hand, is asking for early rewards for denuclearization steps it has taken already that include the dismantlement of its only nuclear test site in northeastern Punggye-ri.

Trump appeared to have welcomed the outcome of the latest inter-Korean summit in a Twitter message that said there will be no more "rocket or nuclear testing" at least for now.

Moon is set to visit New York next week for a bilateral summit with the US president, his office Cheong Wa Dae has said.

The South Korean president is widely expected to urge the US to make some concessions and meet North Korea in the middle.

"Because this issue is not something we can address ourselves, I plan to hold candid talks with Chairman Kim Jong-un on where we can find an intersecting point between the United States' call for denuclearization steps and the North's demand for corresponding steps to guarantee its security and end the hostile relationship (between the US and North Korea)," Moon said before heading into this week's talks with Kim.

Moon and Kim have agreed to meet again in Seoul before the year's end for what would be their fourth bilateral summit. (Yonhap)