Yonhap, South Korea's news agency, said Kim told Tang Jiaxuan, China's state councillor, that: "We have no plans for additional nuclear tests."
The delegation to Pyongyang led by Tang met Kim on Thursday and returned to Beijing later that day.
Chosun Ilbo, a South Korean newspaper, said that Kim had also told the Chinese envoy that "he is sorry about the nuclear test".
Meeting with Condoleezza Rice, the US secretary of state, in Beijing on Friday, Tang said that his trip had "not been in vain".
Tang said that the North Korean leader had raised the possibility that the country would return to arms talks.
He reported that Kim said: "If the US makes a concession to some degree, we will also make a concession to some degree, whether it be bilateral talks or six-party talks."
North Korea has long insisted that the US end a campaign to sever the country's ties to the international financial system.
Rice said on Friday that she had been convinced by talks with Chinese leaders that Beijing was committed to enforcing strong sanctions against North Korea.
Rice, who met with Hu Jintao, China's president, and other leaders on Friday, said they were determined to ensure no illicit materials crossed China's long land border with North Korea, a major conduit for North Korean trade.
China has been very reluctant to clamp trade sanctions on North Korea for fear of weakening the regime's already faltering economy.
It endorsed Saturday's UN Security Council sanctions package against Pyongyang but it has since balked at demands it inspect cargo coming from and going to North Korea.
Rice said the Chinese attitude to its ally of over 50 years had changed dramatically after Pyongyang carried out its nuclear test and she expressed great confidence Beijing would fully implement the sanctions package.
She said: "I think that you will see cooperation on cargo, particularly if there is suspicious cargo.
"I think nobody wants to be on the wrong side of this resolution, in other words having something slipping through because you weren't vigilant about enforcing the resolution."
Rice was in Beijing on the third leg of her four-stop diplomatic mission to rally support for the UN sanctions. She visited Tokyo and Seoul earlier in the week and is scheduled to fly to Moscow on Saturday.