Choi Sung of the ruling Uri Party said in a statement he held talks Sunday night in Beijing with a "key North Korean official" whom he declined to identify.
The official also reportedly said any decision by the North to hold a second nuclear weapons test, following its first on October 9 which sparked world-wide shock and UN sanctions, depended on Washington's attitude.
It was the latest in a series of reports suggesting that the communist state will pull back from the brink of a second test, which would be certain to spark harsher sanctions.
The reports cannot be verified and some officials cast doubt on them.
"It does not matter whether it will be a six-way or bilateral meeting as long as we can verify a US willingness to lift financial sanctions and change its hostile policy towards North Korea," Choi quoted the North Korean official as saying.
Such a stance would be a softening of Pyongyang's previous position that it will never return to the talks unless the US lifts the sanctions first.
"We are saying that we would punish those responsible if there were any evidence of irregular trade related to drugs or counterfeit money at BDA," Choi quoted the official as saying.
Choi, a member of the South Korean foreign relations committee, said the North was reaffirming it would return to six-way talks if the United States sent "a meaningful signal" on BDA.
He said the North had "great expectations" for Assistant Secretary of State Christopher Hill's latest Hong Kong visit to help settle the issue positively.
Hill was in Hong Kong on Sunday to discuss issues including North Korean links with Macau banks.
The official quoted by legislator Choi also reportedly claimed the nuclear test was primarily a bargaining counter rather than purely for weapons development.
"Whether to push ahead with a second nuclear test entirely depends on the US attitude," he was quoted as saying.
Interviewed by AFP by phone from Beijing, Choi again declined to name the official.
"All I can say is that he is in such a responsible position as can freely comment on all matters on US-North Korean relations, North Korea-China and inter-Korean relations," he said.
Japanese envoy Ichiro Aisawa said in Beijing that China is not optimistic about North Korea abandoning its nuclear weapons program or the resumption of six-party talks, but believes it has shown signs of flexibility in ending the crisis.

Copyright AFP (Agence France-Presse), 2006