North Korean leader Kim Jong-un speaks during the ninth session of the 14th Supreme People's Assembly held Sept. 26-27 in Pyongyang, in this captured image from Pyongyang's official Korean Central Television Sept. 28. (For Use Only in the Republic of Korea. Yonhap

The top nuclear envoys of South Korea, the United States and Japan denounced North Korea's constitutional amendment to enshrine its policy on nuclear force, Seoul's foreign ministry said Thursday.

South Korea's chief nuclear negotiator, Kim Gunn, and his U.S. and Japanese counterparts, Sung Kim and Hiroyuki Namazu, respectively, held a conference call to discuss the outcome of Pyongyang's key assembly meeting and their joint response to its growing nuclear threats.

North Korea stipulated the policy of strengthening its nuclear force in its constitution at the 14th Supreme People's Assembly held Tuesday and Wednesday. During the meeting, leader Kim Jong-un said trilateral security cooperation between South Korea, the U.S. and Japan posed "the worst actual threat" and vowed to bolster the country's nuclear capability.

The nuclear envoys strongly condemned North Korea's continued pursuit of nuclear weapons while ignoring the crumbling livelihoods of its people.

"They strongly condemned that North Korea has more openly revealed its nuclear ambition by adopting the constitutional amendment in the Supreme People's Assembly that stipulated its nuclear force policy," the ministry said in a release.

The trio urged Pyongyang to halt its nuclear threats and other provocations, vowing to closely coordinate with the international community to make progress on its denuclearization.

The envoys also agreed to closely monitor for signs of North Korea's third attempt to launch a military spy satellite, and arms trade with Russia following a bilateral summit earlier this month.

They also welcomed the return of U.S. soldier Travis King, who was expelled from North Korea earlier in the day after running across the inter-Korean border in July.

Pvt. King made an unauthorized crossing of the Military Demarcation Line into the North during a tour to the Joint Security Area in the Demilitarized Zone separating the two Koreas, July 18. (Yonhap)