Dai, who delivered a letter to Kim from Hu Jintao, the Chinese president, was accompanied on his visit to Pyongyang by Wu Dawei, China's senior nuclear envoy.
According to Xinhua, Hu's letter said that Beijing would "spare no effort to work with the DPRK [North Korea] to realise this goal [denuclearisation of the peninsula]".
Earlier this week, Washington said it was prepared to hold direct talks with Pyongyang in order to bring it back into the six-party talks.
The US had previously said it would only sit down with North Korean officials for talks including the six-party partners.
Talks on Pyonyang's nuclear programme have unfolded in fits and starts, with North Korea taking some steps to disable its nuclear facilities after agreeing an aid-for-disarmament deal in September 2005.
However, it has carried two nuclear tests since, first in 2006 and then in May this year.
Despite condemnation from the UN Security Council over its nuclear testing, the North followed the test in May with several further missile tests, ratcheting up tension with Japan and South Korea.
Recently, Pyonyang has softened its posture and sought bilateral talks with Washington, while still trying to have the six-party negotiations scrapped.