Kim Jong-un would negotiate if the North’s safety is assured, according to South Korean officials.
The South says the subject was raised when its officials met with the North’s leader, Kim Jong-un, in Pyongyang on Monday, during a rare visit.
They said Mr Kim is also open to US talks, and would pause weapons testing.
In previous programmes to halt its nuclear ambitions, the North has failed to keep its promises.
The leaders of North and South Korea have also agreed to meet at a summit next month, Seoul’s envoy says.
It will be the first such meeting for more than a decade and the first since Kim Jong-un took power in North Korea.
Mr Kim and South Korean President Moon Jae-in will meet on the heavily fortified border next month, at the truce village of Panmunjom. The countries also agreed to open a hotline between the leaders.
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