South Korean President Moon Jae-in and U.S. President Donald Trump reaffirmed their commitment to the bilateral alliance and the final, fully verified denuclearization of North Korea during their summit in Seoul last weekend, the State Department said Tuesday.

Trump's two-day visit to South Korea made headlines for his impromptu, third meeting with North Korean leader Kim Jong-un, which produced an agreement to resume working-level talks on the denuclearization of the North, and his stepping over the inter-Korean border to become the first sitting U.S. president to set foot in the communist nation.

South Korean President Moon Jae-in (R) and U.S. President Donald Trump shake hands after a joint press conference at the presidential office, Cheong Wa Dae, in Seoul on June 30, 2019.

Moon and Trump held talks on Sunday before jointly heading to the Demilitarized Zone separating the Koreas for a historic trilateral meeting with Kim.

In a press release, the State Department said the two leaders "affirmed the unbreakable bond between our two countries and committed to further strengthen our bilateral relationship."

On North Korea, they emphasized the need to continue close coordination.

"Both sides reaffirmed their commitment to achieving the final, fully verified denuclearization of North Korea and to the full implementation of U.N. Security Council resolutions regarding North Korea," the department said, noting the international sanctions imposed on Pyongyang for its nuclear and ballistic missile programs.

Trump remains committed to achieving the goals he and Kim agreed to at their first summit in Singapore in June 2018, including transforming bilateral relations, building lasting peace, and complete denuclearization of the North, it added.

On the allies' joint military exercises, which Trump scaled back after the Singapore summit, both leaders acknowledged their importance in maintaining combined military readiness and supporting peace and stability on the Korean Peninsula.

The two sides also agreed to coordinate with Japan over trilateral security cooperation, including information sharing, high-level policy consultation, and combined exercises, according to the department.

Moon and Trump "reaffirmed that the strong U.S.-ROK alliance is the linchpin of peace and security in the Indo-Pacific" and took steps to deepen security, economic, scientific, health, and cultural cooperation in the region, it said, referring to South Korea by its official name, the Republic of Korea.(Yonhap)

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