The South says it is tired of an approach that lets North get perks for small concessions.
UN ban on North Korean weapons may be working. Should it apply to both nuclear and conventional weapons?
US special envoy Stephen Bosworth is said to have accepted the offer, one of several recent overtures from Pyongyang.
The report was not confirmed by South Korean intelligence sources, but it underlines the uncertainty surrounding the North Korean leader's eventual succession.
The US deployed antimissile defense systems in response to reports that North Korea could launch a long-range missile toward the island early next month.
Russia helped North Korea for decades. But now its influence with the "rogue" nation has waned.
Monday's explosion – the latest in a series of hard-line moves by Pyongyang – may have been 20 times more powerful than its last test in 2006.