South Korean Foreign Minister Ban Ki-moon has said his country wants to intensify diplomacy with North Korea.
S Korea says there is no evidence N Korea has nuclear weapons
He was speaking after talks in Washington in a new round of diplomacy to consider how to respond to North Korea's latest statement.
Last week, North Korea's government explicitly said for the first time it had nuclear weapons.
But South Korea says it is too early to describe North Korea as a state with such weapons.
North Korea also said it was indefinitely pulling out of six-party talks on its nuclear weapons programme.
It wants direct negotiations with the United States, which Washington rejects.
North Korea argues it needs nuclear weapons as protection against what it considers to be an increasingly hostile US.
Mr Ban urged North Korea to resume negotiations "as a responsible member of the international community".
"At this time we need to intensify our diplomatic efforts," Mr Ban said.
"We will continue our efforts through peaceful and diplomatic [means]."
The South Korean Unification Minister Chung Dong-young said there was no conclusive evidence that North Korea had actually made a bomb even though it did possess weapons-grade plutonium.