The agency quoted an unidentified diplomatic source in Beijing as saying: "Kim was known to have clarified his stance that there will be no additional nuclear test."
His remarks came during talks with the Chinese envoy on Thursday, it said.
Tang, the first foreign official to meet Kim since North Korea sparked world outrage and UN sanctions with its atomic test on October 9, said in Beijing on Friday his trip to Pyongyang had not been a waste of time.
"Fortunately my visit this time has not been in vain," Tang told visiting US Secretary of State Condoleezza Rice.
Chinese Foreign Minister Li Zhaoxing also reported some positive elements from the meeting, saying the prospect of quickly resuming stalled six-party talks on the North's nuclear program had been discussed.
"At least it increased mutual understanding," Li told reporters when asked about the meeting.
"Everyone discussed how to restart progress in the six-party talks as quickly as possible."
However Rice said North Korea had offered nothing "particularly surprising" during the meeting earlier this week.
A South Korean newspaper said on Friday that Kim had expressed regret about his country's nuclear test and willingness to return to the disarmament talks if the US eases its pressure.
Chosun Ilbo, also quoting an unidentified diplomatic source in China, said Kim made the remarks to Tang's high-level delegation.
"Chairman Kim conveyed his sorry feelings about the nuclear test," Chosun quoted the source as saying.
"If the United States makes concessions to some degree, so will we, be it either at the bilateral level or the six-party talks."
There has been a series of conflicting reports on whether the North is preparing a repeat test, or a series of repeats.
The deputy head of North Korea's foreign ministry, Li Gun, told the US network ABC this week that a second test would be "natural."
"Even if there is a ... nuclear test, that is natural, so we don't have to care much about this issue. I think the test itself will be natural," he said in Pyongyang.
Asked if the United States should not be surprised by a second test, Li said: "That's right, yes."
Some defence analysts say the North will be obliged to test again to validate the results of its first attempt on October 9, which US officials believe partially failed.
A South Korean foreign ministry spokesman said his office has no related information about the Yonhap report. The United States and other nations have been pushing China, the North's only remaining major ally, to use its influence to curtail Kim's nuclear ambitions.
North Korea agreed at the six-nation forum in September 2005 to scrap its nuclear programmes in exchange for energy aid and security benefits.
But it boycotted the forum two months later in protest at US attempts to curb its access to overseas banks.

Copyright AFP (Agence France-Presse), 2006