But there will also be widespread skepticism among conservatives in Seoul and Washington, with many wondering if the North is simply looking for economic relief after a series of increasingly tough global sanctions slapped on Pyongyang for its illicit weapons programs or more time to develop those weapons.
The eight-member team led by General Kim Yong-Chol crossed the border at around midday, according to a statement by the South Korean Unification Ministry.
North Korea must heed the call by major powers to abandon its nuclear and ballistic missile programmes and allow peace to take root on the divided peninsula, South Korea's foreign minister said on Monday.
Moon spokesman Kim Eui-kyeom said the president urged that U.S. And the US President may find himself one day engaging in "hamburger diplomacy" with the "Little Rocket Man" from Pyongyang.
North Korea's delegation to the games included a diplomat in charge of nuclear talks. Secretary of State Rex Tillerson "has reluctantly accepted his decision and wished him well", Nauert said.
The journey of the North Korean delegation to the South was part of the "Olympic thaw" between the two Koreas which, during the recently concluded PyeongChang Games, have made their greatest rapprochement in years. "It's important the United States and North Korea sit down together quickly", he added. On Tuesday, Japan's Foreign Ministry said a Japanese military plane on Saturday detected a North Korean and a Maldavian-flagged ship conducting what Japan judged to be banned transfers. According to a diplomatic source, the two governments confirmed earlier this month that they will not engage in "dialogue" with North Korea, but could accept a "chat".
In his statement, Moon said he met all eight members of the delegation before speaking with North Korean delegation leader Kim Yong Chol, vice chairman of the Party Central Committee and Ri Son Kwon, chairman of the Committee for the Peaceful Reunification of the Fatherland.
Meanwhile, South Korea's foreign minister said sanctions on Pyongyang were only meant to pressure the country into giving up its nuclear ambitions.
Former deputy assistant secretary of defence for East Asia Abraham Denmark said on Twitter that Mr Yun's departure was "a huge loss for the U.S. government at a critical moment".