"Kim apologized to Beijing for going ahead with its threatened nuclear test on October 9," the source told Chosun Ilbo.
Kim, however, reaffirmed Pyongyang's position that the US needs to back off a campaign to financially isolate the country before returning to six-party nuclear talks, reported the newspaper.
"If the United States gives in to a certain degree, we will also do so, whether it's bilateral talks or six-party talks," the diplomatic source quoted Kim as saying, according to Chosun Ilbo.
State Councillor Tang traveled to Pyongyang Thursday and has returned to Beijing to meet with US Secretary of State Condoleezza Rice on Friday.
Rice is touring Asia to firm up regional pressure on the North over its nuclear programmes.
North Korea has refused to return to nuclear talks, which also include the US, China, Japan, Russia and South Korea, since last November. (DPA)