Kim made the pledge to visiting Chinese envoy Tang Jiaxuan this week, they said citing unnamed diplomatic sources after Japanese officials were briefed on the meeting, Japan's Kyodo and South Korea's Yonhap news agencies said.
Kim told Tang that honouring the joint declaration by the two Koreas was a "dying instruction" of his father and the country's former leader Kim Il-Sung, Kyodo said.
The statement lead Chinese officials to conclude that North Korea was not planning a second nuclear test, South Korea's Yonhap reported.
But Japanese officials remain cautious about Kim's latest remarks, given the North's declared test that followed a similar statement.
US Secretary of State Condoleezza Rice cast doubt on Saturday on a reported apology by North Korean leader Kim to the Chinese delegation for carrying out a nuclear test and a pledge not to carry out additional ones.
"I don't know whether or not Kim Jong-Il said any such thing," Rice told journalists accompanying her on a flight from Beijing to Moscow.

Copyright AFP (Agence France-Presse), 2006