"We are just hoping that some ... working-level talks between the United States and the DPRK [North Korea] will take place soon," Kim said.
The envoy stressed, however, that he does not have a concrete prospect or schedule for such talks.
South Korean President Moon Jae-in said earlier on Monday that North Korea and the United States were preparing to relaunch denuclearization talks and would possibly hold another summit, following the collapse of talks earlier in the year.
Moon called on the international community to respond in kind if Pyongyang moves to denuclearize.
US-North Korea talks on the denuclearization of the Korean Peninsula stalled in February following an unsuccessful summit between the two countries' leaders. On Tuesday, the Yonhap news agency reported, citing South Korea's National Intelligence Service, that denuclearization talks between Pyongyang and Washington could resume in two to three weeks.
On Thursday, US State Secretary Mike Pompeo said that despite Washington's hopes to resume talks with Pyongyang, a meeting had not yet been scheduled.
The situation on the Korean Peninsula significantly improved last year after North Korean leader Kim Jong Un's talks with Moon and US President Donald Trump. In June 2018, Kim and Trump reached an agreement, stipulating that North Korea would make efforts to promote the complete denuclearization of the peninsula in exchange for the freezing of US-South Korean military drills and potential removal of US sanctions.