Mr Kim told visiting South Korean envoys it was his “firm will to vigorously advance” closer ties, the North’s KCNA news agency said.
The North Korean leader hosted a dinner for the delegates on Monday.
It marked the first time officials from Seoul had met Mr Kim since he took office in 2011.
Relations between the two Koreas have warmed following last month’s Winter Olympics, which were held in Pyeongchang in the South.
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.
The US has said it is “cautiously optimistic” about improving North-South contacts but has ruled out formal talks with Pyongyang unless it is ready to give up its nuclear weapons.
North Korea has so far rejected the idea.
Mr Chung and Mr Suh are expected to visit Washington later this week to brief US officials on their talks in the North.
President Moon, the son of refugees from North Korea, was elected last year after a campaign that favoured greater dialogue with North Korea.
Ties between the US and North Korea were particularly tense before the Winter Olympics, with both sides threatening each other with total destruction.
However, the Games saw the two Koreas march together under a single flag – the outcome of the first inter-Korean talks in two years. (Courtesy BBC)