The 10-member South Korean delegation includes two ministerial-level envoys - intelligence chief Suh Hoon and National Security Adviser Chung Eui-yong.
Mr Chung had earlier told reporters he would deliver President Moon Jae-in's "resolution to maintain the dialogue and improvement in relations between the South and the North... [and] to denuclearize the Korean peninsula".
Following the meeting, KCNA said Kim Jong-un had "warmly welcomed" the delegates and held an "openhearted talk" with them.
"Hearing the intention of President Moon Jae-in for a summit from the special envoy of the south side, he [Kim Jong-un] exchanged views and made a satisfactory agreement," the report said.
"He gave the important instruction to the relevant field to rapidly take practical steps for it."
During the two-day visit, the South Korean group is focusing on establishing conditions for talks aimed at getting rid of the North's nuclear weapons as well as dialogue between the US and Pyongyang.